Saved Bookmarks
| 1. |
The product of three consecutive terms of a GP is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an AP. Then the sum of the original three terms of the given GP is: (a) 36 (b) 32 (c) 24 (d) 28A. 36B. 28C. 32D. 24 |
|
Answer» Correct Answer - B Let the three consecutive terms of a GP are `(a)/(r)`, a and ar. Now, according to the question, we have `(a)/(r).a.ar = 512` `rArr a^(3) = 512` `rArr a = 8`...(i) Also, after adding 4 to first two terms, we get `(8)/(r) + 4, 8 + 4, 8r` are in AP `rArr 2(12) = (8)/(r) + 4 + 8r` `rArr 24 = (8)/(r) + 8r + 4 " " 20 = 4 ((2)/(r) + 2r)` `rArr 5 = (2)/(r) + 2r " " 2r^(2) - 5r + 2 = 0` `rArr 2r^(2) - 4r - r + 2 = 0` `rArr 2r (r -2) - 1 (r -2) = 0` `rArr (r - 2) (2r -1) = 0` `rArr (r -2) (2 -1) = 0` `rArr r = 2, (1)/(2)` Thus, the terms are either 16, 8 4 or 4, 8, 16. Hence, required sum = 28 |
|