Question

The first three terms of a geometric sequence are x, y, z and these have the sum equal to 42. If the middle term y is multiplied by 5/4, the numbers x, $\frac{5y}{4}$, z now form an arithmetic sequence. The largest possible value of x, is-

• A. 6
• B. 12
• C. 24
• D. 20

Answer 1

Answer: (C)

24

Answer 2

The three terms of the geometric sequence with the common ratio r, are x, xr, xr²

\ x + xr + xr² = 42

After multiplying the middle term by $\frac{5}{4}$will get an arithmetic sequence.

This yields $\frac{5}{4}$xr – x = xr² – $\frac{5}{4}$xr

After cancelling x, we obtain a quadratic equation

2r² –5r + 2 = 0, with roots r = $\frac{1}{2}$and r = 2.

On substituting these in x + xr + xr² = 42,

We get x = 6 or 24