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?