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 a40 when a1 = 1000, r = - 1/2

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 a40 when a1 = 1000, r = - 1/2

Accepted Answer

Hello. Today we're going to be finding the specified term of a geometric sequence Using the given first term and common ratio. So the common ratio given to us is r is equal to negative 1/3 which for the convenience of this problem, I'm going to write as negative 1/3 And we are given the first term a sub one which is equal to 6000. And we are asked to use this information to find the 25th term of the geometric sequence. Now, in order to find the 25th term, we're going to need to find the general formula for the term of a geometric sequence. And that is given to us as a sub N is equal to our first term. A sub one times. The common ratio are raised to the power of n minus one. So we're going to need three things in order to use this formula. We're going to need our first term, our common ratio and end, The only thing we're missing is N. But since we are asked to find the 25th term of the geometric sequence, we're going to allow N2 equal to 25. So now we just have to plug in these three pieces of information into our general formula and we can use that to find the 25th term. So doing so is going to give us a sub 25 is equal to a sub one which is 6000 Times are common ratio which is negative 1/3 race the power of N -1 which is 25 -1. Now, 25 -1 is going to give us 24. So we have negative 1/3 race of the power of 24. And using our exponential rule, we're going to distribute this exponent of 24 to both the numerator and denominator. Doing this is going to give us 6000 times negative one to the power of 24. Since 24 is an even number, negative one to the power of an even number is going to produce a positive number one. So we have 1/3 to the power of 24. And multiplying these values together is going to give us Over three to the power of 24. Now, at this point you should just go ahead and plug this into a calculator and plugging this into a calculator is going to give you a fraction with a denominator of 94 million, 94 billion 143 million and the numerator of 2000 and this is going to be the 25th term of the geometric sequence. And with that being said, the answer to this problem is going to be d So I hope this video helps you in understanding how to approach a geometric sequence problem and I'll go ahead and see you all in the next video

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 a40 when a1 = 1000, r = - 1/2

Verified Solution

Key Concepts

Geometric Sequence

General Term Formula

Common Ratio