Sequences Review

Front

What is a geometric sequence?

Back

A 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

t(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

Identify the common ratio in the geometric sequence: 3, 6, 12, 24...

Back

The common ratio is 2.

Front

What is an arithmetic sequence?

Back

A sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Front

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

Back

t(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

Identify the common difference in the arithmetic sequence: 5, 8, 11, 14...

Back

The common difference is 3.

Front

What is the first term of the geometric sequence: -2, -10, -50, -250...?

Back

The first term is -2.

Front

How do you find the 37th term of the arithmetic sequence: -38, -48, -58, -68...?

Back

Use the formula: t(37) = -38 + (37-1)(-10) = -398.

Front

What type of sequence is 400, 200, 100, 50, 25...?

Back

It is a geometric sequence.

Front

What is the common ratio of the sequence: 256, 64, 16, 4...?

Back

The common ratio is 1/4.