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 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

How do you find the common difference in an arithmetic sequence?

Back

The common difference (d) is found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

Front

Find the 25th term of the sequence if a_1 = 5 and d = 0.5.

Back

The 25th term is 17.

Front

What is the common difference in the sequence: 29, 21, 13, 5, ...?

Back

The common difference is d = -8.

Front

Find the common difference in the sequence: -18, -23, -28, -33, ...

Back

The common difference is d = -5.

Front

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

Back

The next three terms are 3, 12, 21.

Front

If a_1 = 10 and d = 2, what is the 10th term?

Back

The 10th term is 28.

Front

What is the 5th term of the sequence if a_1 = 4 and d = 3?

Back

The 5th term is 16.

Front

How do you determine if a sequence is arithmetic?

Back

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