Arithmetic vs. Geometric

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 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

Identify the common difference in the sequence: 3, 7, 11, 15.

Back

The common difference is 4.

Front

Identify the common ratio in the sequence: 2, 6, 18, 54.

Back

The common ratio is 3.

Front

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

Back

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

Front

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

Back

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

Front

What is the sum of the first n terms of a geometric sequence?

Back

The sum (S_n) can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.

Front

What is the difference between arithmetic and geometric sequences?

Back

Arithmetic sequences use addition/subtraction to find the next term, while geometric sequences use multiplication/division.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

Back

The 10th term is 32.