Arithmetic and Geometric Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

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

Back

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

Front

Given the sequence 6, 11, 16, 21, what is the common difference?

Back

The common difference is 5.

Front

How do you find the 25th term of an arithmetic sequence?

Back

Use the formula a_n = a_1 + (n-1)d. For a_1 = 5 and d = 0.5, a_25 = 5 + (25-1)0.5 = 17.

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.

Front

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

Back

The formula is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Which type of sequence has a common difference?

Back

Arithmetic sequence.

Front

Is the sequence 14, 22, 30, 38 an arithmetic sequence?

Back

Yes, it is an arithmetic sequence with a common difference of 8.

Front

Is the sequence 7, 9, 12, 16 geometric?

Back

No, it is not a geometric sequence.

Front

What is the common difference in the sequence 10, 15, 20, 25?

Back

The common difference is 5.