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 3n^{2}+ 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

** **

- How many two-digit numbers are divisible
by 3?
- Which term of A.P
:3,8,13,18,…………………,is 78?
- Check whether –150 is a term of the A.P
11,8,5,2………
- 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?
- The 8
^{th} term of an AP is
zero. Find the ratio of its 38^{th} term and 18th term.
- Which term of A.P is 3,15,27,39……. will
be 132 more then its 54
^{th} terms?
- Find the 20
^{th} terms from the
last terms of the A.P: 3,8,13,…………..253.
- Determine the 15
^{th} and 5^{th}
term from the end of the A.P.: 4,9,14,…….,254.
- Which term of A.P.
:9,13,17,21,25……………………is 109.
- If the 8
^{th} terms of an A.P.is
31 and the 15^{th} terms is 16 more than the 11^{th}
terms.
- 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.
- 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.
- How many numbers of two digits are
divisible by 7 ?
- Find the number of integers b/t 49 to
500 which are divisible by 7?
- 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.
- 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.
- 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.
- The sum of three numbers in A.P. is – 3
,and their product is 8. Find the numbers.
- If 2x,x + 10, 3x + 2 are in A.P., Find
the value of x.
- For what value of n ,the n
^{th}
terms of the arithmetic progressions 63,65,67……..and 3,10,17,…………are
equal?