Question

The 8th term of a GP is -7/32 find its common ratio if its first term is 28

Answer 1

Common ratio = -1/2

Step-by-step explanation:

       $\text{8}^{th}$ term of a Geometric progression is given as $\dfrac{-7}{32}$. The first term is given as $28$.

       Any general Geometric progression can be represented using the series $a,ar,ar^{2},ar^{3},ar^{4}...\text{ }ar^{n-1}$.

The first term in such a GP is given by $a$, common ratio by $r$, and the $n^{th}$ term is given by $ar^{n-1}$.

       In the given GP, $a=28;t_{8}=ar^{7}=\dfrac{-7}{32}\\\\28r^{7}=\dfrac{-7}{32}\\\\r^{7}=\dfrac{-1}{128}\\\\r=\dfrac{-1}{2}$

∴ Common ratio is $\dfrac{-1}{2}$.