Question

The first, second and fourth term proportion are 6 ,18,and 25 respectively find its third term

Answer 1

$\huge\text{\underline{\underline{Given:}}}$

$\sf{First\:term}$ = 6

$\sf{Second\:term}$ = 18

$\sf{Third\:term}$ = ?

$\sf{Fourth\:term}$ = 25

$\text{\underline{Let\:the:}}$

First term be 'p'. (where p = 6)

Second term be 'q'. (where q = 18)

Third term be 'r'. (where r = x)

Fourth term be' s'. (where s = 25)

So,

$\text{\underline{Here,\:we\:can\:say\:that,}}$

p : q = r : s

$\text{\underline{And\:we\:get,}}$

$\frac{p}{q} = \frac{r}{s}$

$\boxed{p \times s = r \times q}$

$\text{\underline{We\:know\:that,}}$

Product of extreme terms = Product of means term

$\text{\underline{Now,}}$

$p \times s = r \times q$

$6 \times 25 = x \times 18$

$x = \frac{6 \times 25}{18}$

$x =\boxed{ \frac{25}{3}}$

$\text{\underline{Therefore,}}$

The third term proportion is $\boxed{ \frac{25}{3}}$.