Arithmetic Sequence Math Example 5

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Find the sum of the first 20 terms of the arithmetic sequence: 5, 8, 11, 14, ...

1
Identify the first term $a_1 = 5$ and the common difference $d = 8 - 5 = 3$ .
2
Find the 20th term: $a_{20} = a_1 + (20 - 1)d = 5 + 19 \times 3 = 5 + 57 = 62$ .
3
Apply the sum formula: $S_{20} = \frac{n}{2}(a_1 + a_n) = \frac{20}{2}(5 + 62) = 10 \times 67 = 670$ .

Answer

S_{20} = 670

The sum of an arithmetic sequence uses the formula

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

, which pairs the first and last terms, the second and second-to-last terms, and so on — each pair has the same sum.

About Arithmetic Sequence

A sequence where each term is obtained from the previous by adding a fixed constant called the common difference $d$ .

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