Question

sum of first and the third terms in a G.P. is 15 and that of the 5th and 7th terms is 240.Find the 9th term of
the G.P.​

Answer 1

Answer:

Let a be the first term of the G.P and r be the common ratio.

According to the question.

Sum of First and Third Term is 15.

a + ar^{2}=15

a(1+r^{2})= 15

(1+r^{2})=15/a --------- let it be our eqn 1.

Sum of 5th and 7 th term is 240.

ar^{4} + ar^{6}=240

ar^{4}(1+r^{2})=240 ------from our eqn 1.

ar^{4} * (15/a) = 240

r^{4}*15=240

r^{4}=240/15

r^{4}=16

r^{2}= 4,-4

but a square cannot be negative therefore

r^2 = 4

On subtituting the value of r ^{2} on the eqn 1

a(1+r^{2})= 15

a*5=15

a=3.

Now the 9 th term will be

ar^{8}

a (r^2)^{4}.

3 * 4^{4}= 768.