Question

find 10th term and nth term of GP 5,25,125

Answer 1

ANSWER :–

▪︎10th term of G.P. is 97,65,625.

EXPLANATION :–

GIVEN :–

▪︎ A Geometrical progression series =》 5,25,125,.........

TO FIND :–

10th term of G.P.

SOLUTION :–

☞ We know that –

• If first term of G.P. is a , common ratio is r and total terms is n . Then nth term is –

$\\ \implies{ \boxed{ \bold{ a_{n} = a {r}^{n - 1} }}}$

▪︎ In the given series –

• first term(a) = 5

• common ratio(r) = 25/5 = 5

▪︎ Now let's find 10th term –

$\\ \implies{ \bold{ a_{10} = 5 {(5)}^{10 - 1} }}$

$\\ \implies{ \bold{ a_{10} = 5 {(5)}^{9} }}$

$\\ \implies{ \bold{ a_{10} = {(5)}^{10} }}$

$\\ \implies{ \bold{ a_{10} =9765625 }}$

Hence, 10th term of G.P. is 97,65,625