Arithmetic Sequences

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 increases or decreases by in an arithmetic sequence.

Front

Find the common difference: 2, 5, 8, 11, ...

Back

d = 3

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

Find the 10th term of the sequence: 4, 7, 10, ...

Back

The 10th term is 34.

Front

Is the sequence 10, 15, 20, 25, ... arithmetic?

Back

Yes, it is arithmetic.

Front

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

Back

The sum S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

Front

Find the next three terms in the arithmetic sequence: 1, 4, 7, ...

Back

The next three terms are 10, 13, 16.

Front

Determine if the sequence 12, 9, 6, 3, ... is arithmetic.

Back

Yes, it is arithmetic with a common difference of -3.

Front

What is the common difference of the sequence: 15, 10, 5, 0, ...?

Back

d = -5