Sequence and Series Review

Front

Is the sequence 2, 4, 12, 48,... geometric?

Back

No, this sequence is not geometric because the ratio between consecutive terms is not constant.

Front

What is the common ratio for the sequence: 28, 14, 7, 3.5...?

Back

The common ratio is 1/2.

Front

-21, -16, -11, -6,... Is this sequence arithmetic, geometric, or neither?

Back

This sequence is arithmetic with a common difference of d = 5.

Front

In what type of sequence do you ADD a constant value to the previous term?

Back

Arithmetic sequence.

Front

Find the sum for the following series: 1 + 2 + 3 + ... + 20

Back

The sum is 210.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term is given by a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the formula for the sum of the first n terms of an arithmetic series?

Back

The sum is S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a constant called the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply to get from one term to the next.

Front

Find the common ratio for the sequence: 3, 6, 12, 24...

Back

The common ratio is 2.