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 = 3, r = 2

Accepted Answer

Welcome back. I'm so glad you're here. We've got a couple of properties of a geometric sequence and we are to find the first five terms of that sequence. That means we are looking for a sub one value of the first term. A sub to value 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. And were given a sub one. We can just fill that right in. Under a sub one. A sub one is one. Were also given the ratio R. equals four. The ratio is important because that's the value that we take and multiply to the previous terms value to get our new value and I'll show you what that looks like. So to find a sub two, we're going to take the previous term which is one and we're going to multiply that times are ratio So to find a sub two, we take one times four and that gives us four To find a sub three. We take the previous terms value which is four. And we multiply that by our ratio four times 4 gives us 16 To find a sub four. We take the previous terms value that's 16 and we multiply it by our ratio. So we've got 16 times four. That gives us 64 to find our fifth terms value. We take the previous term 64 multiply that times are ratio 64 times four and that gives us 256. Writing these all on one line. We've got a sub one is one, A sub two is four, A sub three is 16, A sub four is 64 and a sub five is 256. We look at our answer choices and this matches with answer choice a well done. We'll catch you on the next one.

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