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 = \frac{n}{2} \times (2a_1 + (n-1)d), where S_n is the sum, n is the number of terms, a_1 is the first term, and d is the common difference.

Front

If a_1 = 22, d = -8, and n = 21, what is S_n?

Back

S_n = -1218.

Front

Evaluate the arithmetic series: 2 + (-2) + (-6) + (-10)..., S_{10}.

Back

S_{10} = -160.

Front

What is the common difference in the series: 11 + 18 + 25 + 32...?

Back

The common difference d = 7.

Front

Back

The sum is 63.

Front

What is the nth term of an arithmetic sequence?

Back

The nth term can be calculated using the formula a_n = a_1 + (n-1)d.

Front

Back

The sum is 365.

Front

What is the first term of the series if a_1 = 22 and d = -8?

Back

The first term a_1 is 22.

Front

If the common difference d is negative, what does that indicate about the arithmetic series?

Back

It indicates that the terms of the series are decreasing.