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 = \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.