Question

The first three terms of 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 number $x$, $\frac{5y}{4}$, $z$ now form an arithmetic sequence . The largest possible value of $x$, is

• A. $6$
• B. $12$
• C. $24$
• D. $20$

Answer 1

The correct option is C $24$

Given,

First three terms of geometric sequence $=x,y,z$

Sum of the three terms $=42$

The three terms of the geometric sequence with the common ratio $r$ will be $=x,xr,x{r}^2=42$

On multiplying the middle term by $\frac{5}{4}$, we will get the arithmetic sequence as $-\frac{5}{4}xr-x=x{r}^2-\frac{5}{4}xr$

Therefore,

$2r^2-5r+2=0$

$r=\frac{1}{2},2$

On substituting the values in equation $x+xr+x{r}^2=42$, we will get

$x=6$ or $24$

Thus, the largest value of $x=24$