Class 10 AP test full marks- 40

1. Can 2n^2 - 7 be the nth term of AP?  [2]
2. Show that the sum of (m+n)th and (m−n)th term of an A.P. is equal to twice the mth term. [4]
3. If the sum of first 7 terms of an AP is 49 and sum of 17 terms is 289, find the sum of first n terms. [3]
4. In an A.P. the first term is 25, n th term is −17 and the sum of n terms is 132. Find n and the common difference.  [3]
5. Divide 96 into four parts which are in A.P. and the ratio between the product of their means to the product of their extremes is 15:7. Find AP     [4]
6. If the sum of first m terms of an AP be n and the sum of its first n terms be m then show that the sum of its first (m+n) terms is −(m+n).   [extra]
7. How many three digit Numbers are divisible by 87?  [3]
8. In an AP ten times of its tenth term is equal to thirty times of 30th term. Find 40th term?  [3]
9. The first term of an A.P is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P. [3]
10. The fourth term of an A.P. is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P and the sum of first 50 terms. [4]
11. In an A.P, if mth term is n and nth term is m, show that its rth term is (m + n - r). [3]
12. Given AP is 21,18,15....-81 Can any term of series be zero if yes find the no of terms. [2]
13. The sum of the 2nd term and the 7th term of an A.P is 30. If its 15th term is 1 less than twice of its 8th term, find the A.P [3]
14. If 7 times the 7th term of an AP is equal to 11 times the 11th term, show that the 18th term of it is 0  [3]