Q&A for How to Find Any Term of a Geometric Sequence

You can't do it, because that is neither a geometric nor an arithmetic sequence.

Take this for example. If you have given a3 = 27 and r = 3, divide 27 by 3, which is 9. Divide again by 3 and get 3. Then you have a1 = 3, a2 = 9, and a3 = 27. If you know the constant and one term in the geometric sequence, you can calculate any other term in the sequence.

If you are given any term in the sequence, treat it as if it's the first term, and proceed as usual from there. If you're not given any terms in the sequence, you cannot find the nth term.

There is no last term. Numbers are infinite, so the sequence goes on forever.

f(n) = (n-1)*r f(n) = (n-1) *1/5 f(1)=500 r is the common ratio and f1 is the first term. (n-1) is the previous term.

You would also have to know r, the common ratio between consecutive terms. Then use the formula for finding the sum of a geometric sequence to solve for the first term.

Usually, a given formula will help you find the first term. If there are no given formulas, the first term will often be given.

P=n*y, where P = total number of people, n = number of tables and y = number of people per table.

It can't be done.

You can't find n unless you also know the nth term.

In this example r = 1. The usual formula for the sum of the first n terms of a geometric sequence does not work when r = 1. Instead, the sum is simply 3 multiplied by n.

Consider the last term to be the nth term. Then use the equation: nth term = (a)[r^(n-1)]. Plug in the known values to solve for n.

Use a calculator. The process remains the same no matter how large the numbers are.

Because that is not a geometric sequence, you can't find the nth term. In a geometric sequence each term (except the first) is found by multiplying the preceding term by a given constant. (The sequence you've proposed is derived by multiplying the preceding term by 2 and then adding 1.)

You're given the eighth term. So 16,807 = (a)[r^(n-1)] = (32)(r^7). Divide by 32: 525.22 = r^7. That involves a difficult calculation, but once you find r, you would multiply it by 32 to find the first unknown term, and keep multiplying by r to find the five other unknown terms.

You can't find the missing terms unless you also know either the ratio or the number of terms in the sequence.

An= Asub1(R^n-1), so if my Asub1 is 2 and my common ration (R) is 4, my A sub 7 would be like this: Asub7=2(4^7-1).

Use the formula An=A1(R^n-1), then substitute.

The same way. Treat fractions as you would any other number in a geometric sequence. Presumably you know how to multiply/divide fractions. So you just do the division/multiplication parts with fractions instead of whole numbers.

Divide it by its preceding numbers to find the common ratio and if this is the same for all the numbers given in that example, then that number is the common ratio. For example: in 2,4,8,16,16 divided by 8 = 2 and 8 divided by 4 = 2 and 4 divided by 2 = 2.

Since there are 3 terms, you are going to find S3 in which the formular is a[(r^n)-1]/r-1 when the magnitude of r is greater than 1.

The difference between terms is 7. The difference between 15 and 78 is 63. Divide 7 into 63 to get 9, which is the number of terms in that sequence between 15 and 78.

The nth term is (n+4). There is no "formula" for this. The question can be answered "by inspection" only. (That means just looking at the situation and figuring out what's required.)

Assuming that's a geometric sequence, you go from 90 to 30 by dividing 90 by 3, and you go from 30 to 10 by dividing 30 by 3. If you divide 10 by 3, you get 10/3 for the fourth term, and then you get 10/9 for the fifth term.

To get from 4 to -12, you have to multiply by (-3). Likewise, to get from -12 to 36, you have to multiply by (-3). So obviously, the common ratio in the sequence is -3. Therefore, the next term in the sequence is (36)(-3) = -108.

The numbers are 3, 9 and 27. You would probably have to use "trial and error" here, starting with a common ratio of 2 and then trying 3. It would help to recognize that (3)(3) = 9, and (9)(9) = 81.

That's not a geometric sequence, so the formula given above does not apply.

We don't have enough information to do that. We'd need the first term or the common ratio.