Arithmetic and Geometric Sequences S1 Review

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

Front

How do you find the next term in an arithmetic sequence?

Back

To find the next term in an arithmetic sequence, add the common difference to the last term. For example, in the sequence 5, 8, 11, the next term is 11 + 3 = 14.

Front

How do you find the next term in a geometric sequence?

Back

To find the next term in a geometric sequence, multiply the last term by the common ratio. For example, in the sequence 2, 4, 8, the next term is 8 * 2 = 16.

Front

What is the common difference in the sequence 10, 7, 4, 1?

Back

The common difference is -3, as each term decreases by 3.

Front

What is the common ratio in the sequence 1, 3, 9, 27?

Back

The common ratio is 3, as each term is multiplied by 3 to get the next term.

Front

Is the sequence 5, 10, 15, 20 arithmetic or geometric?

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The sequence is arithmetic because the difference between consecutive terms is constant (5).

Front

Is the sequence 2, 6, 18, 54 arithmetic or geometric?

Back

The sequence is geometric because each term is multiplied by 3 to get the next term.

Front

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

Back

The nth term of an arithmetic sequence can be found using the formula: 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 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 and r is the common ratio.