In Exercises 1–8, write the first five terms of each geometric se...

Question

In Exercises 1–8, write the first five terms of each geometric sequence.a1 = 5, r = 3

Accepted Answer

Hello. Today we're going to be using the given information to find the first five terms of the geometric sequence. So what we are given is the first term which is a sub one is equal to two and were given a common ratio which is r is equal to four. Now, in order to find any term of a geometric sequence, we need to use the general formula for the term of a geometric sequence that is given to us as a sub N Is equal to the first term. A sub one times the common ratio are raising the power of N -1. Now here we're going to need our first term our common ratio and N but N is going to change depending on what term we're looking for. So let's just go ahead and jump into this process. We're going to start by finding our second term since we're already given our first term so far. Second term, we're going to allow N two equal to two and that's going to give us a sub two is equal to our first term which is two times the common ratio. Four race the power of n minus one, which is two minus one Now, 2 -1 is just going to give us one. So we're not going to need the exponent here because any number raised to one is just itself and what we are left with is two times four, which is going to give us eight and that's going to be the second number in the geometric sequence. Next let's go ahead and fight the third for the third number we're going to let N is equal to three. And when N is equal to three we get a sub three is equal to two times four. Race of the power of three minus one which is squared is going to give us 16. So we have two times 16 which is going to give us and that's going to be the third term of the sequence. Next, for the fourth term we're going to let N is equal to four and that's going to give us a sub four is equal to two times four, raised to the power of 4 -1 which is three. Now, two times four cubed is going to give us 128 and that's going to be the fourth term in the geometric sequence. And finally, for the fifth term we have N is equal to five and that's going to give us a sub five is equal to two times four to the power of five minus one, which is four and two times four raised to the power four is going to give us 512 and that's going to be the final term that we need for the first five terms of the geometric sequence. So let's just go ahead and list out the terms now we were told that the first term is to then we calculated the rest of the terms the second term was eight. The third one was 32 The 4th 1 was 128 and the final one was 512. With that being said. This is the first five terms of the geometric sequence with the given first term and the common ratio. And with that being said, the answer to this problem is going to be be 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.

In Exercises 1–8, write the first five terms of each geometric sequence.a1 = 5, r = 3

Key Concepts

Geometric Sequence

First Term (a1)

Common Ratio (r)

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