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, 
, z now form an arithmetic sequence. The largest possible value of x, is-
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The three terms of the geometric sequence with the common ratio r, are x, xr, xr 2
∴ x + xr + xr 2 = 42
After multiplying the middle term by 
will get an arithmetic sequence.
This yields 
xr – x = xr 2 – 
xr
After cancelling x, we obtain a quadratic equation
2r 2 –5r + 2 = 0, with roots r = 
and r = 2.
On substituting these in x + xr + xr 2 = 42,
We get x = 6 or 24
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