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.28
- C.32
- D.24
Show answer and solution
Correct option: B
Solution
Let the three terms of the GP be a/r, a, ar. Their product = a³ = 512, so a = 8.
The three GP terms are 8/r, 8, 8r. After adding 4 to the first two, the AP is: (8/r + 4), 12, 8r.
For AP: 2(12) = (8/r + 4) + 8r → 24 = 8/r + 8r + 4 → 20 = 8/r + 8r → 8r² - 20r + 8 = 0 → 2r² - 5r + 2 = 0 → r = 2 or r = 1/2.
Taking r = 2: terms are 4, 8, 16. Sum = 28.
The three GP terms are 8/r, 8, 8r. After adding 4 to the first two, the AP is: (8/r + 4), 12, 8r.
For AP: 2(12) = (8/r + 4) + 8r → 24 = 8/r + 8r + 4 → 20 = 8/r + 8r → 8r² - 20r + 8 = 0 → 2r² - 5r + 2 = 0 → r = 2 or r = 1/2.
Taking r = 2: terms are 4, 8, 16. Sum = 28.
[JEE Main 2019 · 12 Jan · Shift I]