In Exercises 31–34, write the first five terms of each geometric ...

Question

In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 1/2, r = 1/2

Accepted Answer

Welcome back. I'm so glad you're here. We've got a couple of properties of geometric sequence and we are to find the first five terms of that sequence. So we're trying to find a sub one value of the first term. A sub to the value of the second term. A sub three. The value of the third term. A sub four. The value of the fourth term and a sub five. Well we've already got the value of the first term, that's one of our givens ye a sub one equals one third. So I'm just going to write that down Right below a sub one. And we're also given this ratio. The ratio is important because that's the number we are going to multiply by the previous terms value in order to get our new term. So putting that into practice to find a sub to to find the second term. We're going to take a sub one. We're going to take that 1/3 and we're going to multiply it by our ratio. So 1 3rd times 1 6th And we know that 1/3 times 1/6 is 1/18. And again to find the third terms value. We're going to take the previous terms value. 1/18 and multiply it by that ratio. So 1/18 times 1/6. And we know that that is one 108th. To find the fourth terms value. We're going to take the third terms value which is 1/108. And we're going to multiply it by the ratio which is 1/ When we multiply those together that gives us 1 648th. And to find the fifth terms value. We take the previous terms value which is 1 648th and multiply it by our ratio times 1/6. And we know using a calculator that that is 1/3888. So writing those all out together are a sub one. Our first term is one third. Second term is 1/18. 3rd term is one 108th. Third or fourth term is one 648th and our fifth term is one 3888th. We look at our answer choices and that matches with answer choice. C. Well done. We'll catch you on the next one.

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