Assignment-A.P

1. Do any two consecutive terms of an A.P can be equal ?
2. If the first term of an A.P is a and the common difference is d, what will be the 4thterm of the sequence?
3. How many 2-digit numbers are divisible by 3?
4. If in an A.P, first term is 5 , common difference is 5 and the last term is 60, then find the sum of first n terms.
5. Find the next term of given A.P. √8, √18, √32, √50,………..
6. Find the next term of the given A.P.3,3,3,3,3,3,3,………….
7. Find the first negative term of the A.P. 114, 109, 104,…
8. Which term of A.P. -2, 3, 8, 13,… is 78?
9. Which term of sequence 22, 19, 16,… is the first negative term?
10. Find the 6th term from end of the A.P. 17, 14, 11…-40.
11. Find the sum of first 40 positive integers divisible by 3.
12. How many terms of the A.P. 3,5,7,9,… must be added to get the sum 120?
13. Find the number of terms in an A.P, in which the a=5, common difference=3 and the last term =83
14. The sum of the first 30 terms of an A.P. is 1635.if its last term is 98,find the first term and the common difference of the given A.P.
15. If the 3rd and the 9th terms of an A.P. are 4 and -8 respectively. Which term of the A.P. will be 0?
16. If the mth term of an AP is 1/n and the nth term is 1/m. Show that the sum of (mn) terms is (mn+1)/2
17. If the sum of m terms of an AP is the same as the sum of its n terms. Show that the sum of its (m+n) terms is zero.
18. If the numbers a, b, c, d, e forms an AP , then find the value of a – 4b + 6c – 4d + e
19. The sum of n, 2n, 3n terms of an AP are S1 , S2, S3 respectively. Prove that
S3 = 3 ( S2 - S1)
20. Find the four number in AP whose sum is 20 and sum of whose squares is 120.
21. Find the number of integers between 50 and 500 divisible by 5.
22. Find the number of terms in the sequence
20 , 19 1/3 , 18 2/3 ,......................... of which the sum is 300. Explain the double answer.
23. In an AP, the sum of first n terms is (3n2 + 5n ) / 2. Find the 25th term.
24. The sum of n terms of three AP are S1 , S2 and S3. The first term of each is unity and the common difference are 1,2 and 3 respectively. Prove that S1 + S3 = 2S2