In Exercises 17–24, write a formula for the general term (the nth...

Question

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence.18, 6, 2, 2/3, ...

Accepted Answer

Hello today we're going to be finding the formula for the nth term of the given geometric sequence. And then we're going to use that formula to find the eighth term of the sequence. So in order to find the formula for the N term, we need to use the general formula for the nth term. And the general formula is going to be a to the sub N is equal to the first term. A sub one times your common ratio arm raised to the power of n minus one. So we're going to need to fill in a couple of things in order to use this to find the eighth term. First thing we need is to find the first term of the geometric sequence and we're going to need to use the common ratio of the geometric sequence. Well we know what the first term of the geometric sequence is going to be. It's given to us here as 56. So we're going to allow a sub one to equal to 56. Next we need to find the common ratio which is our. And the common ratio is just any term in the geometric sequence divided by its previous term. So here we can take the second term of the sequence. A sub two and divided by the first term. A sub one. A sub two is 14 and a sub one is 56. So if we take 14 and divided by 56 we get a common ratio of 1/4. Now let's go ahead and plug this into the general formula for the N term. So that way we can get a formula we can use to find the eighth term of the sequence. So a sub N is going to equal to a sub one which is 56 times your common ratio, which is 1/4 raised to the power of n minus one. And this is going to be the formula we need in order to find the eighth term of our of our geometric sequence. Now let's go ahead and use this formula. Since we want to find the eighth term, we're going to allow N2 equal to eight since N represents the amount of terms in your given sequence. So allowing end to be equal to eight is going to give us a sub eight is equal to 56 times 1/4, raised to the power of n minus one, which is going to be eight minus one and eight minus one gives us seven. So we have 56 times one. Fourth race of the power of seven. Now, using our exponential rule, we're going to distribute the seventh exponent to both the numerator and denominator. One race of the power of seven is just going to be one and four race of the power of seven is going to give us 16,384. So we have 56 times one over 16, 384, multiplying this together is going to give us 56 over 16,384 and that's going to simplify to seven over 2048 this is going to be the eighth term in the geometric geometric sequence. So just to recap, our general formula for the nth term is a sub. N is equal to 56 times one to the 1/4 race the power of n minus one and the eighth term is seven over 2048. With that being said, the answer to this problem is going to be C. 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.

Struggling with College Algebra?

In Exercises 17–24, write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for a_n to find a7, the seventh term of the sequence.18, 6, 2, 2/3, ...

Watch next

Geometric Sequences practice set