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.
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