Geometric Series

Front

What is a geometric series?

Back

A geometric series is the sum of the terms of a geometric sequence, where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

How do you find the first four terms of a geometric sequence given a formula?

Back

Substitute n = 1, 2, 3, and 4 into the formula a_n to find the first four terms.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio (r) is the factor by which we multiply each term to get the next term in the sequence.

Front

Is the sequence {14, 22, 30, 38, ...} arithmetic or geometric?

Back

It is an arithmetic sequence with a common difference (d) of 8.

Front

What is the explicit formula for the geometric sequence with a first term of 3 and a common ratio of -4?

Back

The explicit formula is a_n = 3 * (-4)^(n-1).

Front

How do you determine if a sequence is arithmetic, geometric, or neither?

Back

A sequence is arithmetic if the difference between consecutive terms is constant, geometric if the ratio of consecutive terms is constant, and neither if neither condition holds.

Front

If Daisy received $2 on her first birthday and the amount tripled each year, how much will she receive on her 5th birthday?

Back

She will receive $2 * 3^4 on her 5th birthday.

Front

What are the next three terms in the geometric sequence: 512, 256, 128, ...?

Back

The next three terms are 64, 32, and 16.

Front

What is the sum of the first n terms of a geometric series?

Back

The sum S_n of the first n terms can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where r is not equal to 1.