Arithmetic Sequence and Series

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 common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term in the sequence increases or decreases by.

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 and d is the common difference.

Front

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

Back

The sum of the first n terms (S_n) is given by the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

Front

Given the sequence: 25, 21, 17, 13,... what is the common difference?

Back

The common difference is -4.

Front

What is the explicit formula for the sequence: 2, 8, 14,...?

Back

The explicit formula is a_n = 6n - 4.

Front

How do you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is constant.

Front

What is the sum of the first 21 terms of the series 22 + 14 + 6 + (-2) + ...?

Back

The sum is -1218.

Front

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

Back

The 5th term is 22.

Front

How many terms are in the arithmetic sequence: 5, 10, 15, ..., 100?

Back

There are 20 terms.