Sequences

Front

Is the sequence geometric? If so, identify the common ratio: 6, 12, 24, 48.

Back

Yes, the sequence is geometric with a common ratio of 2.

Front

What is the eleventh term of an arithmetic sequence in which a1 = 3 and d = 6?

Back

The eleventh term is 63.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

An arithmetic sequence has a common difference, while a geometric sequence has a common ratio.

Front

Find the missing term in the geometric sequence: 8, 20, 50, 125, _____.

Back

The missing term is 312.5.

Front

Describe the pattern in the sequence: 13, 15, 17, 19,... Find the next three terms.

Back

Add 2; the next three terms are 21, 23, 25.

Front

Define an arithmetic sequence.

Back

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

Front

Define 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 an arithmetic sequence?

Back

The nth term (an) is given by an = a1 + (n-1)d, where a1 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 (an) is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

Front

If the first term of a geometric sequence is 3 and the common ratio is 4, what is the fifth term?

Back

The fifth term is 3 * 4^(5-1) = 768.