Question

If the sum of three numbers in a G.P. is 26 and the sum of products taken two at a time is 156, then the numbers are

• A. 2,6,18
• B. 1,8,64
• C. 1,5,25
• D. 1,4,1

Answer 1

Answer: (A)

2,6,18

Let the terms be $\frac{a}{r},a,ar$
Given $a(\frac{1}{r}+1+r)=26$
Also $a^2(\frac{1}{r}+1+r)=156$
Dividing both equations we get $a=6$
And substituting $a=6$ in one of the given equations, we get

$36(\frac{1}{r}+1+r)=156$

$\therefore (\frac{1}{r}+1+r)=\frac{156}{36}=\frac{13}{3}=\frac{1}{3}+1+3$

so we can write $r=3$
So, the terms are $\frac{a}{r},a,ar$ i.e $2,6,18$.