Sequence and series Session-1

Sequence and Series Session-1

Try these Problems :

1. The sum of the three consecutive numbers in GP. is 21 and the sum of their squares is 189.   The product of the numbers is

(A) 72                  (B) 216                (C) 108                (D) 144

2. If the 1Oth term of the sequence, a, a - b, a - 2b, a - 3b,.....is 20 and the 20th term is 10, then the x^th term of the series is

(A) 10 – x             (B) 20 – x           (C) 29 – x             (D) 30 – x

3. Given that 1² + 2² + 3² +.....+ 20² = 2870, the value of 2² + 4² + 6² + ....... + 40²is:

(A) 11480            (B) 5740              (C) 28700            (D) 2870

4. Which of the following numbers belong to the series? 4, 11, 18, 25, 32, 39, .......

(A) 2099              (B) 2096              (C) 2098              (D) 2097

5. A man starts going for morning walk every day. The distance walked by him on the first day was 2 kms. Everyday he walks half of the distance walked on the previous day. What can be the maximum total distance walked by him in his life time?

(A) 4 kms.            (B) 120 kms.       (C) 18 kms.          (D) Data inadequate

6. The number of terms in the sequence 4,11,18,......... 186 is

(A) 17                  (B) 25                   (C) 26                   (D) 27

7. The sum 5³ + 6³ +.....+ 10³ is equal to

(A) 2295              (B) 2425              (C) 2495              (D) 2925

8. The sum 9 +16+25 + 36 +.....+ 1OO is equal to

(A) 350                (B) 380                (C) 400                (D) 420

9. If the 4th term of an arithmetic progression is 14 and 12th term is 70, then the first term is

(A) -10                 (B) -7                    (C) +7                   (D) +10

10. The middle term of arithmetic series 3, 7, 11 ... 147, is

(A) 71                  (B) 75                   (C) 79                   (D) 83

11. The sum to 200 terms of the series 1 + 4 + 6 + 5 + 11 + 6 + .......... is

(A) 30,400           (B) 29,800           (C) 30,200           (D) None of these

12. If the sum of the series 54 + 51 + 48 + ........... is 513, then the number of terms are

(A) 18                  (B) 20                   (C) 17                   (D) None of these

13. There are 60 terms in an A.P. of which the first term is 8 and the last term is 185. The 31^st term is

(A) 56                  (B) 94                   (C) 85                   (D) 98

14. If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are-

(A) 5,10,15,20    (B) 4,10,16,22     (C) 3,7,11,15       (D) None of these

15. The number of terms of the series 5, 7, 9, .... that must be taken in order to have sum of 1020 is

(A) 20                  (B) 30                   (C) 40                   (D) 50

16. The number of two digit numbers which are divisible by 3 is

(A) 33                  (B) 31                   (C) 30                   (D) 29

17. If the nth term of an A.P. is 4n + 1, then the common differ­ence is:

(A) 3                     (B) 4                     (C) 5                     (D) 6

18. The number of common terms to the two sequences 17, 21, 25, ....., 417 and 16, 21, 26, ........, 466 is

(A) 19                  (B) 20                   (C) 21                   (D) 91

19. The fourth, seventh and tenth terms of a GP. are p, q, r respectively, then :

(A) p² = q² + r²   (B) q² = pr         (C) p² = qr            (D) pqr + pq + 1 = 0

20. Find the value of 1³ + 2³ + 3³ +... + 15³.

(A) 11025            (B) 13400            (C) 900                (D) 14400

21. The sum of 40 terms of an AP whose first term is 4 and common difference is 4, will be:

(A) 3280              (B) 1600              (C) 200                (D) 2800

22. In a GP, the first term is 5 and the common ratio is 2. The eighth term is:

(A) 640                (B) 1280              (C) 256                (D) 160

23. If the arithmetic mean of two numbers is 5 and their geomet­ric mean is 4, then the numbers are:

(A) 4,6                 (B) 4,7                  (C) 3,8                  (D) 2,8

24. The value of (1³ + 2³ + 3³ + .... + 15³) – (1 + 2 + 3 + .... 15) is

(A) 14280            (B) 14400           (C) 12280            (D) 13280

25. The sum of the 6^th and 15^th terms of an arithmetic progres­sion is equal to the sum of 7^th, 10^th and 12^th terms of the same progression. Which term of the series should neces­sarily be equal to zero ?

(A) 10^th                           (B) 8^th                            (C) 1^st                              (D) None of these

 Answers