Arithmetic and Geometric Sequences

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 common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

What is an arithmetic sequence?

Back

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

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the amount added to each term to get the next term in an arithmetic sequence.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

Find the 22nd term of the arithmetic sequence: 5, 8, 11, ...

Back

68

Front

Identify the common difference in the sequence: 97, 86, 75, 64, ...

Back

-11

Front

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...

Back

-146

Front

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

Back

The sum can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.