Guess paper 10th Chapter_Arithmetic Progression

10th Math : Arithmetic Progression : Guess paper part-II

1.        Find the sum of 20 terms of the A.P. 1,4,7,10………

2.        If the nth terms of an A.P is (2n + 1), find the sum of first n terms of the A.P.

3.        Find the sum of first 30 terms of an A.P.whose second term is 2 and seventh term is 22.

4.        Find the sum of first 10 terms of an A.P., in which 3^rd term is 7 and 7^th term is two more than thrice of its 3^rd term.

5.        Find the sum of all even integers between 2 to 100 divisible by 2.

6.        Find the number of terms in the series 20, 19 1/3 + 18 2/3 +………of which the sum is 300,explain the double answer.

7.        If the mth term of an A.P. is 1/n and the nth terms is 1/m, show that the sum of mn terms is ½(nm + 1).

8.        If the sum of n terms of an A.P.is same as the sum of its n terms, show that the sum of its (m + n) terms is zero.

9.        Find the sum of first n odd natural numbers.

10.     If the 8^th terms of an A.P.is 31 and the 15^th terms is 16 more than the 11^th terms find the sum of first 20 terms.

11.     How many terms of A.P.: 24,21,18,…….. Must be taken so that their sum is 78?

12.     The angles of a triangle are in AP.If the greatest angle equals the sum of the other two, find the angles.

13.     Find the sum of two digits numbers, which are divisible by 7?

14.     Find the sum of number b/t 49 to 500 which are divisible by 7?

15.     If the p^th term of an A.P.is q and the q^th term is p, prove that its n^th term is (p + q – n) and find the sum of first (p+q)^th term .

16.      How many terms of the sequence 18,16,14…… should be taken so that their sum is zero.

17.     Write the first 5 terms of an AP whose nth term is given by (2n+1)/3.

18.     How many terms in the sequence -6  , -11/2 , -5 , -9/2 , …are needed to give the sum 0 ?

19.     Find the sum of all the natural numbers less than 100 which are divisible by 6.

20.     The sum of n terms of an A.P.; be 3n2 – n and its common difference is 6,find its first and 27^th term.

21.     The sum of nth terms of an A.P. is 3n²+ 5n, then find its nth term.

22.     Find the sum of first 21 terms Ö2 + Ö8 + Ö18 + Ö32………….

ARITHMETIC PROGRESSIONS MATHEMATICS CASS X- Guess paper part-II

                                                                                                 

1. How many two-digit numbers are divisible by 3?
2. Which term of A.P :3,8,13,18,…………………,is  78?
3. Check whether –150 is a term of the A.P 11,8,5,2………
4. If 3^rd and 9^th terms of an A.P are 4 and – 8 respectively, which term is 106.find the 29^th term?
5. The 8^th term of an AP is zero. Find the ratio of its 38^th term and 18th term.
6. Which term of A.P is 3,15,27,39……. will be 132 more then its 54^th terms?
7. Find the 20^th terms from the last terms of the A.P: 3,8,13,…………..253.
8. Determine the 15^th and 5^th term from the end of the A.P.: 4,9,14,…….,254.
9. Which term of A.P. :9,13,17,21,25……………………is 109.
10. If the 8^th terms of an A.P.is 31 and the 15^th terms is 16 more than the 11^th terms.
11. If 10^th term of an A.P is 52 and 17^th terms is 20 more than the 13^th terms find the A.P.
12. Determine the general terms of A.P. whose 7^th terms is – 1 and 16^th term 17.also find it’s 25^th term.
13. How many numbers of two digits are divisible by 7 ?
14. Find the number of integers b/t 49 to 500 which are divisible by 7?
15. If the p^th term of an A.P.is q and the q^th term is p, prove that its n^th term is (p + q – n ) and (p+q)^th term is zero.
16. If m times the m^th term of an A.P. is equal to n times the n^th term, show that the (m+n)^th terms of an A.P is zero.
17. The 4^th term of an A.P. is three times the first and 7^th term exceeds twice the third term by 1.find the A.P.
18. The sum of three numbers in A.P. is – 3 ,and their product is 8. Find the numbers.
19. If 2x,x + 10, 3x + 2 are in A.P., Find the value of x.
20. For what value of n ,the n^th terms of the arithmetic progressions 63,65,67……..and 3,10,17,…………are equal?

CBSE ADDA: X Arithmetic progression assignment

Q. 1 How many terms of A.P. 22, 20, 18, . . . . . . . . should be taken so that their sum is zero?
Q. 2 Find the sum of odd positive integers less than 199. 
Q. 3 How many two digits numbers between 3 and 102 are divisible by 6? 
Q. 4 If 7 times the 7th term is equal to 11 times the 11th term of an A.P. Find its 18th term. 
Q. 5 Which term of A.P. 13, 21, 29, . . . . . . will be 48 less than its 19th term? 
Q. 6 Find the A.P. whose 3rd term is –13 and 6th term is +2. 
Q. 7 Find the A.P., whose 5th term is 23 and 9th term is 43. 
Q. 8 The angles of a triangle are in A.P. If the smallest angle is one fifth the sum of other two angles. Find the angles. 
Q. 9 Aditi saved Rs. 500 in the first month of a year and then increased her monthly savings by Rs. 50. If in the nth month, her monthly savings become Rs 1000. Find the value of 'n'. 
Q. 10 The sum of first n terms of an A.P. is 2n2 + n . Find nth term and common deference of the A.P. 
Q. 11 The sum of 3rd and 7th terms of an A.P. is 14 and the sum of 5th and 9th terms is 34. Find the first term and common difference of the A.P. 
Q. 12. Find the sum of the first 30 terms of an A.P., whose nth term is 2–3n. If mth and nth terms of an A.P. are 1/n and1/m respectively, then find the sum of mn terms 
Q. 13 If mth , nth and rth terms of an A.P. are x, y and z respectively, then prove that :- m( y – z) + n(z – x) + r (x – y) = 0 
Q. 14. If the roots of the equation a(b – c) x2 + b(c – a) x + c (a – b) = 0 are equal, then show that 1/a , 1/b , 1/c are in A.P. 
Q. 15. If the sum of m terms of an A.P. is n and the sum of n terms is m, then show that sum of (m +n) terms is – ( m + n).

CBSE MATH STUDY: X Arithmetic progression assignment:(For next set of 20 Questions)

CLASS 10 Maths Guess Questions Chapter Arithmetic ...

CBSE MATH STUDY: CLASS 10 Maths Guess Questions Chapter Arithmetic ...1) For what value of p, are 2p-1, 7 and 3p three consecutive terms of an A.P? (P=3)

2) Find the value of k, so that 3k + 7, 2k +5, 2k + 7 are in A.P (k= -4)

3) Find the 15^th term from the end of the A.P: 3, 5, 7,………, 201(173)

4) Find the 11^th term from the end of the A.P: 10, 7, 4,……, - 62 (-32)

5) If Sn_, the sum of first n terms of an A.P is given by Sn = 3n² – 4n, then find its nthterm

(6n – 7)

6) The sum of n terms of an A.P. is 3n² + 5n. Find the A.P. Hence, find its 16^th term

(6n + 2, 98)

7) In the following A.P. find the missing term -, 38, -, - , - , -22

8) Find the sum of all natural numbers less than 100 which are divisible by 6 (816)

9) Find the sum of 3 digit numbers which are not divisible by 7 (424214)

10) Find the sum of all three digit numbers which leave the remainder 3 when divided by 5 (99090)

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CBSE10th Arithmetic Progression Study material

1. An 

1.Arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number d to the preceding term, except the first term.
2. The difference between the two successive terms of an A.P. is called the common difference.
3. Each of the number in the list of arithmetic progression is called a term of an A.P.
4. The arithmetic progression having finite number of terms is called a finite arithmetic progression.
5. The arithmetic progression having infinite number of terms is called an infinite arithmetic progression.

Arithmetic Progression CBSE Class X Self Evaluation Tests For Mathematics

1. 0, –4, –8, –12, ............

2.. 1, 2, 4, 8, 16, ...............

3. 6, 6, 6, 6, 6, ............

4. 5, 5 +Ö 3, 5  2 Ö3, 5+3Ö3,...........

7. Find the sequence whose of nth term is given by :

(a) 2n – 7 (b) –3 + 5n² (c) 4/3 - 6n  Also, determine which of these sequences are A.P’s.

8. Find the A.P. whose nth term is given by :

(a) 9 – 5n (b) –n + 6 (c) 2n + 7

9. Find the 8th term of an A.P. whose 15th term is 47 and the common difference is 4.

10. The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term and the general term.

11. The 7th term of an A.P. is – 4 and its 13th term is –16. Find the A.P. [CBSE 2004]

12. Which term of the A.P. 3, 10, 17, .... will be 84 more than its 13th term? [CBSE 2004]

13. Find the A.P. whose third term is 16 and the seventh term exceeds its fifth term by 12.

14. For what value of n is the nth term of the following A.P.’s the same?

1, 7, 13, 19, ..... and 69, 68, 67............... [CBSE 2006C]

15. If the 10th term of an A.P. is 52 and 17th term is 20 more than the 13th term, find the A.P.

16. If seven times the seventh term of an A.P. is equal to nine times the ninth term, show that 16th term is zero.

17. (a) Which term of the A.P. 2, 6, 10, 14, ....... is 78?

(b) Which term of the A.P. 5, 9, 13, 17, ....... is 125?

(a) Which term of the A.P. –4, –1, 2, 5, ....... is 119?

(a) Which term of the A.P. Ö2, Ö18, Ö50 ....... is 21 Ö2 ?

18. How many terms are there in each of the following finite A.P.’s?

(a) –3, –4, –5, –6, ....., – 107

(b) 7, 13, 19, ........, 211

(c) 8, 13, 18, ......., 208

19. (a) Is 216 a term of A.P. 3, 8, 13, 18, ......?

(b) Is 271 a term of A.P. 1, 4, 7, 10, .....?

(c) Is –52 a term of A.P. 10, 7, 4 ......?

(d) Is –190 a term of A.P. –3, –8, –13, ......?

20. Find the 8th term from the end of the A.P. 7, 10, 13, ..... , 184. [CBSE 2005]

21. Find the 20th term from the end of the A.P. 3, 8, 13, ....., 253.

22. Find the value of k so that k – 3, 4k – 11 and 3k – 7 are three consecutive terms of an A.P.

23. Find the value of x so that 3x + 2, 7x – 1 and 6x + 6 are three consecutive terms of an A.P.

24. The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the

first term and the common difference.

25. The 9th term of an A.P. is equal to 7 times the 2nd term and 12th term exceeds 5 times the 3rd term by 2. Find

the first term and the common difference.

26. Find the middle term of an A.P. with 17 terms whose 5th term is 23 and the common difference is –2.

27. For what value of n, the nth terms of the two A.P.’s are same? 2, –3, –8, –13, ...... and –26, –27, –28, –29, .......

28. For what value of n, the nth terms of the two A.P.’s are same? 3, 10, 17, ...... and 63, 65, 67, .....

29. Find the number of integers between 200 and 500 which are divisible by 7.

30. How many numbers of three digits are exactly divisible by 11?

31. The angles of a triangle are in A.P. If the greatest angle equals the sum of the other two, find the angles.

32. Three numbers are in A.P. If the sum of these numbers is 27 and the product is 648, find the numbers.

33. If m times the mth term of an A.P. is equal to n times its nth term, show that the (m + n)th term of the A.P. is

zero.

34. A sum of Rs. 1000 is invested at 8% simple interest per annum. Calculate the interest at the end of 1, 2, 3,

......years. Is the sequence of interest an A.P.? Find the interest at the end of 30 years.

35. Two A.P.’s have the same common difference. The difference between their 100th terms is 111222333.

CBSE10th Class Solved Paper - Arithmetic Progression

1. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Solution: 12 = a + 2d

106 = a + 49d

So, 106-12 = 47d

Or, 94 = 47d

Or, d = 2

Hence, a = 8

And, n₂₉ = 8 + 28x2 = 64

2. If the 3rd and the 9th terms of an AP are 4 and -8 respectively, which term of this AP is zero?

Solution: -8 = a + 8d

4 = a + 2d

Or, -8 – 4 = 6d

Or, -12 = 6d

Or, d = -2

Hence, a = -8 + 16 = 8

0 = 8 + -2(n-1)

Or, 8 = 2(n-1)

Or, n-1 = 4

Or, n = 5

3. The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

Solution: n₇ = a + 6d

And, n₁₀ = a + 9d

Or, a + 9d – a – 6d = 7

Or, 3d = 7

Or, d = 7/3

4. Which term of the AP: 3. 15, 27, 39, … will be 132 more than its 54th term?

Solution: d = 12,

132/12 = 11

So, 54 + 11 = 65th term will be 132 more than the 54th term.

5.  How many three digit numbers are divisible by 7?

Solution: Smallest three digit number divisible by 7 is 105

Greatest three digit number divisible by 7 is 994

Number of terms

= {(last term – first term )/common difference }+1

= {(994-105)/7}+1

= (889/7)+1=127+1=128

6. How many multiples of 4 lie between 10 and 250?

Solution: Smallest number divisible by 4 after 10 is 12,

The greatest number below 250 which is divisible by 4 is 248

Number of terms: {(248-12)/4}+1

{236/4}+1 = 59+1 = 60

7. For what value of n, are the nth terms of two APs: 63, 65, 67,… and 3, 10, 17,… equal?

Solution: In the first AP       a = 63 and d = 2

In the second AP                 a = 3 and d = 7

As per question,

63+2(n-1) = 2+ 7(n-1)

Or, 61 = 5 (n-1)

Or, n-1 = 61/5

As the result is not an integer so there wont be a term with equal values for both APs.

8. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

Solution: As the 7th term exceeds the 5th term by 12, so the 5th term will exceed the 3rd term by 12 as well

So, n₃ = 16

n₅ = 28

n₇ = 40

n₄ or n₆ can be calculated by taking average of the preceding and next term

So, n₄ = (28+16)/2 = 22

This gives the d = 6

AP: 4, 10, 16, 22, 28, 34, 40, 46, ……..

9. Find the 20th term from the last term of the AP: 3, 8, 13, ……, 253.

Solution: a = 3, d = 5

253 = 3 + 5(n-1)

Or, 5(n-1) = 250

Or, n-1 = 50

Or, n = 51

So, the 20th term from the last term = 51 – 19 = 32nd term

Now, n₃₂ = 3 + 5x31 = 158

10. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and the 10th terms is 44. Find the first three terms of the AP.

Solution: a + 3d + a + 7d = 24

Or, 2a + 10d = 24

Similarly, 2a + 14d = 44

So, 44 – 24 = 4d

Or, d = 5

2a + 10x5 = 24

Or, a + 25 = 12

Or, a = -13

So, first three terms of AP: -13, -8, -3,

11. Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reached Rs. 7000.?

Solution: 7000 = 5000 + 200(n-1)

Or, 200(n-1) = 2000

Or, n-1 = 10

Or, n = 11

12. Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her savings become Rs. 20.75, find n.

Solution: 20.75 = 5 + 1.75(n-1)

Or, 1.75(n-1) = 15.75

Or, n-1 = 9

Or, n = 10

For more papers visit  CBSE: 10th Class Sample Test Paper- Arithmetic Progression

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