Q26Multiple choice
(M.C.Q.). 17. If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is
- (A)3
- (B)2
- (C)6
- (D)4 SEQUENCE AND SERIES 163 18. The third term of G.P. is 4. The product of its first 5 terms is (A) 43 (B) 44 (C) 45 (D) None of these 19. If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is (A) 0 (B) 22 (C) 220 (D) 198 20. If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is 1 1 (A) 3 (B) (C) 2 (D) 3 2 21. If in an A.P., Sn = q n2 and Sm = qm2, where Sr denotes the sum of r terms of the A.P., then Sq equals q3 (A) (B) mnq (C) q 3 (D) (m + n) q2 22. Let Sn denote the sum of the first n terms of an A.P. If S2n = 3Sn then S3n : Sn is equal to (A) 4 (B) 6 (C) 8 (D) 10 x 1–x 23. The minimum value of 4 + 4 , x ∈ R, is (A) 2 (B) 4 (C) 1 (D) 0 24. Let Sn denote the sum of the cubes of the first n natural numbers and sn denote the sum of the first n natural numbers. Then equals r =1 sr n(n + 1)(n + 2) n(n + 1) (A) (B) 6 2 n 2 + 3n + 2 (C) (D) None of these 25. If tn denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t50 is (A) 492 – 1 (B) 492 (C) 502 + 1 (D) 492 + 2 26. The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cm3 and the total surface area is 252cm2. The length of the longest edge is (A) 12 cm (B) 6 cm (C) 18 cm (D) 3 cm Fill in the blanks in the Exercises 27 to 29. a −b