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 a12 when a1 = 5, 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 we are given is the first term, a sub one which is equal to four. And were given the common ratio which is negative three. We want to use this to find the 15th term of the geometric sequence. Now, in order to find the 15th term of the geometric sequence, we want to use the general formula for the nth term of geometric sequence that is given to us as a sub, N is equal to our first term, A sub one times the common ratio are raised to the power of n minus one. So here we're going to need a sub one. We're going to need our and we're going to need N. Since we are asked to find 1/15 term of the geometric sequence, we're going to let n equal to 15. So we're just gonna take these three pieces of information and plug them into the general formula for the nth term. That way we can find the 15th term of the sequence. And doing so is going to give us a sub 15 is equal to our first term, which is four times the common ratio, which is negative three raised to the power of n minus one which is 15 minus one. Now, 15 -1 is going to give us 14. So we have four times negative three raised to the power of 14. And plugging this into a calculator is going to give us the value of 19, 19,131, and this is going to be the 15th term for the geometric sequence. And with that being said, the answer to this problem is going to be a so I hope this video helps you in understanding how to approach a 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 a12 when a1 = 5, r = - 2