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

Front

If a_1 = 5 and d = 3, what is the 10th term of the arithmetic sequence?

Back

The 10th term a_{10} = a_1 + (10-1)d = 5 + 9 \times 3 = 32.

Front

Calculate the sum of the first 10 terms of the series: 2 + 5 + 8 + ...

Back

S_{10} = \frac{10}{2} \times (2 + 29) = 5 \times 31 = 155.

Front

What is the common difference in the arithmetic series: 4, 7, 10, 13, ...?

Back

The common difference d = 7 - 4 = 3.

Front

Given a_1 = -3, d = 2, find S_n if n = 7.

Back

S_7 = \frac{7}{2} \times (2 \times -3 + (7-1) \times 2) = \frac{7}{2} \times (-6 + 12) = \frac{7}{2} \times 6 = 21.

Front

What is the 5th term of the arithmetic sequence where a_1 = 10 and d = -2?

Back

a_5 = a_1 + (5-1)d = 10 + 4 \times (-2) = 10 - 8 = 2.

Front

If S_n = 100, a_1 = 10, and d = 5, how many terms are in the series?

Back

Using S_n = \frac{n}{2} \times (2a_1 + (n-1)d), we solve for n: 100 = \frac{n}{2} \times (20 + (n-1) \times 5).

Front

Evaluate the series: 1 + 4 + 7 + ... + 28.

Back

This is an arithmetic series with a_1 = 1, d = 3, and n = 10. S_{10} = \frac{10}{2} \times (1 + 28) = 5 \times 29 = 145.

Front

What is the formula to find the nth term of an arithmetic sequence?

Back

The nth term a_n = a_1 + (n-1)d.