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 = 1 000 000, r = 0.1

Accepted Answer

Hello. Today we're going to be finding a specified term for an unknown geometric sequence. Using the given first term. And the common ratio. So the common ratio given to us is R is equal to 0. and the given first term is 200 million. And we are asked to use this to find a sub 12 which is the term of our geometric sequence. Now, in order to find the 12 term, we're going to use the general formula for the nth term of the geometric sequence. And that is given to us as a sub, N is equal to our first term, a sub one times our common ratio race of the power of n minus one. So here we're going to need three things. We're going to need our first term, our common ratio and we're going to need N. Since we are asked to find the 12 term of the geometric sequence, we're going to allow N- two equal to 12. So plugging in these three values into our general and term formula is going to give us a sub 12 is equal to our first term which is 200 million Times The Common Ratio which is 0.2 raised to the power of N -1 which is 12 -1. Now, all we need to do is to go ahead and simplify 12 -1 is going to give us 11. So we have 0.2 raised to the power of 11. And at this point you can go ahead and plug in this entire thing into a calculator. And it should give you the approximate value of 4.096, and this is going to be the 12th term of the given of the unknown 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 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 = 1 000 000, r = 0.1