Geometric Sequences

Tyler, Chelsea and Michelle

Formula for the Sum of the First n Terms of a Geometric Sequence

A geometric sequence is a sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant. The amount by which we multiply each time is called the common ratio of the sequence.

The common ratio, r is found by dividing any term after the first term by the term that directly precedes it.

1) If you don't know the first term in the sequence, but you know the common ratio, the last term and the number of terms in the series you can find the first term for a

like in the following equation:

last term = a (common ratio ^ (number of terms - 1))

tn = arn - 1

2) Find the number of terms in your sequence: Call this number n. You may be able to just count the terms, but in most cases you'll need to do some work to figure it out.

3)If you do not know the number of terms, but you know the last term, referred to as tn the first term, and the common ratio you can solve for n using the following equation:

last term = first term (common ratio ^ (n-1))


tn = arn - 1

4) Solve for the sum. The sum is referred to as Sn. Insert your values into the following equation:

sum of series = first term ( 1 - common ratio ^ number of terms) / (1 - common ratio)



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