The second and fifth term of a geometric progression are 1 and⅛ respectively find the first term

Answer 1

Let the first term be $a$ and the common ratio be $r$. Then we have:

Second term: $ar$
Fifth term: $ar^4$

It is given that:

$ar=1$
$ar^4=\dfrac{1}{8}$

Dividing the second equation by the first, we get:

$r^3=\dfrac{1}{8}$

$r=\dfrac{1}{2}$

Substituting this value of $r$ in the first equation, we get:

$a(\dfrac{1}{2})=1$

$a=2$

Therefore, the first term is $\boxed{2}$.