Arithmetic Sequences 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 (d) is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

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

Back

The nth term (a_n) 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 arithmetic sequence: 3, 7, 11, 15...

Back

The 10th term is 39.

Front

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

Back

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

Front

If a_1 = 4 and d = 3, what is the 15th term?

Back

The 15th term is 46.

Front

What is the common difference in the sequence: 10, 15, 20, 25...?

Back

The common difference is 5.

Front

Find the next term in the sequence: 2, 5, 8, 11...

Back

The next term is 14.

Front

What is the 5th term of the sequence if a_1 = 2 and d = 4?

Back

The 5th term is 18.

Front

How do you determine if a sequence is arithmetic?

Back

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