Arithmetic sequences

Japanese school year: Math B

What you learn

Learn how to find the general term and the sum of arithmetic sequences. This concept is widely used to analyze steady patterns and compute cumulative totals. Basic knowledge of linear algebraic expressions will help you better understand and apply the formulas.

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Key points

Formula to find the $n$ -th term $a_n$ of an arithmetic sequence starting at $a_1$ with common difference $d$ . It adds $d$ exactly $n - 1$ times to $a_1$ .

a_n = a_1 + (n - 1)d

Formula to calculate the total sum $S_n$ of the first $n$ terms in an arithmetic sequence, computed as $\text{number of terms} \times (\text{first term} + \text{last term}) / 2$ .

S_n = \frac{1}{2}n(a_1 + a_n) = \frac{1}{2}n\{2a_1 + (n - 1)d\}

When three numbers $a, b$ , and $c$ form an arithmetic sequence in order, twice the middle term $b$ equals the sum of the ends $a + c$ .

2b = a + c

Choose a set to practice.

Practice 1Coming soon