Question

the 4term of a geometric sequence is equal to 8times it's first term. if the 6 term is 64, find its 10term.​

Answer 1

ANSWER :-

How can I answer this question on GP? Given that the 4th term is 6 and the 7th term is 48, what is the sequence?

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We know that nth term of a GP =a∗rn−1 where a is the first term and r is the common ratio

So 7 th term =a∗r7−1=a∗r6 this tells us;

a∗r6=48

And 4 th term =a∗r4−1=a∗r3

This again tells us,

a∗r3=6

We know have a pair of equations and we need to solve for a and r. We can simple divide both equations to solve for r first;

a∗r6a∗r3=486

r3=8

r=2.

Now let's replace this to get a;

a∗23=6

a∗8=6

a=68

a=34

Therefore the GP =3∗rn−14

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