Question

Sum of infinite terms of a GP is 12. If the first term is 8, what is the 4th term of this GP​

Answer 1

Answer:

$\Large{\mathsf{a_4 = {\dfrac{8}{9}}}}$

Explanation:

Formula for sum of infinite terms of a G. P. is

$\Large{\mathsf{S = {\dfrac{a} { 1 - r}}}}$

$\mathsf{12 = {\dfrac{8} { 1 - r}}}$

12( 1 - r) = 8

12 - 12r = 8

12r = 12 - 8

r = 1/3

Common Ratio of the G. P. is 1/3

For the 4th term of G. P.,

$\Large{\mathsf{a_4 = ar^{(n-1)}}}$

$\mathsf{a_4 = 8* {\dfrac{1}{3^{(4-1)}}}}$

$\mathsf{a_4 = {\dfrac{8}{3^3}}}$

$\Large{\mathsf{a_4 = {\dfrac{8}{9}}}}$