Arithmetic Series

Front

What is an arithmetic series?

Back

An arithmetic series is the sum of the terms of an arithmetic sequence, where each term after the first is obtained by adding a constant difference to the previous term.

Front

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

Back

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

Front

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

Back

The 10th term a_10 = a_1 + (n-1)d = 5 + (10-1)3 = 32.

Front

Evaluate the arithmetic series: 11 + 18 + 25 + 32..., S_7

Back

224

Front

Evaluate the arithmetic series: 0 - 7 - 14 - 21..., S_17

Back

-952

Front

If a_1 = 5 and a_n = 145, find S_15.

Back

1125

Front

Evaluate the arithmetic series: 28 + 38 + 48 + 58..., S_7

Back

406

Front

Evaluate the arithmetic series: 14 + 23 + 32 + 41..., S_11

Back

649

Front

What is the common difference in the arithmetic series 3, 7, 11, 15?

Back

The common difference is 4.

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 d is the common difference.