Question

If the second term of G.P. is 2 and the sum of infinity is 8, find the first term.

Answer 1

let a be the first term and r be the common difference.

Then $ar=2$

$r=\frac{2}{a}$

sum of infinity is 8

i.e $\frac{a}{1-r}=8$

$\frac{a}{1-\frac{2}{a}}=8$

$\frac{a^2}{a-2}=8$

$a^2=8a-16$

$a^2-8a+16=0$

$(a-4{)}^2=0$

Thus $a-4=0$

$a=4$