In Exercises 9–16, use the formula for the general term (the nth ...

Question

In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r.

Find a8 when a1 = 6, r = 2

Accepted Answer

Hello. Today we're going to be finding the specified term using the given first term. And the common ratio of a geometric sequence. So what is given to us is the first term. A sub one is equal to negative five And were given the common ratio which is seven. We want to use this information to find the sixth term sub six in the geometric sequence. Now, in order to find any term in the geometric sequence, we need to use the general formula for the NTT term and that is given to us as a sub. N is equal to your first term. A sub one times the common ratio. Our race of the power of N -1. So here we're going to need three things. We're going to need a sub one. We're going to need our and we're going to need N. While since we are asked to find the sixth term of the geometric sequence, we're going to let N equal to six. Now we're going to take these three pieces of information and plug them into the general formula. And that's going to give us a sub six is equal to the first term, which is negative five times seven. Race to the power of n minus one which is six minus one Now, 6 -1 is just going to give us five. So we have negative five times seven. Race of the power of five and seven rates of the power of five is going to give us 16,807. So we have negative five times 16,807. And multiplying these values together is going to give us negative 84,035 and that is going to be the sixth term in the geometric sequence. And with that being said, the answer to this problem is going to be D. So I hope this video helps you in understanding how to approach this geometric sequence problem, and I'll go ahead and see you all in the next video.

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In Exercises 9–16, use the formula for the general term (the nth term) of a geometric sequence to find the indicated term of each sequence with the given first term, a1 and common ratio, r. Find a8 when a1 = 6, r = 2