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,5y/4,z now form an arithmetic sequence. The largest possible
value of x is​

Answer 1

Answer:

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Answer 2

The largest possible value of x is 42.

First three terms of geometric sequence = x y and z ( Given)

Sum of the three terms = 42 ( Given)

The three terms of the geometric sequence with the common ratio r will be = x, xr, xr² =42

On multiplying the middle term by 5/4, we will get the arithmetic sequence as - 5/4 xr −x = xr²−5/4xr

Therefore,

2r²−5r+2=0

r = 1/2 and r=2

On substituting the values in equation x+xr+xr² = 42, we will get

x = 6 or 24

Thus, the largest value of x is 42.