What is the sum of the arithmetic sequence 22, 13, 4?

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What is the sum of the arithmetic sequence 22, 13, 4?

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Answer 1 · 2014-09-27T15:52:47

$22 + 13 + 4 = 39$ $22 + 13 + 4 = 39$ . A very straightforward answer.

However, if one wishes to find it that way (the stupid way), then first notice that this is a simple arithmetic series. Use the formula $S = \frac{n}{2} (a_{1} + a_{n})$ $S = n/2 (a_1 + a_{\text{n}))$ or the formula $S = \frac{n}{2} (2 a_{1} + (n - 1) d)$ $S = n/2 (2a_1 + (n-1)d)$ where $a_{1}$ $a_1$ is the first term, $a_{n}$ $a_n$ is the last term, $d$ $d$ is the common difference, $n$ $n$ is the number of terms in your series.

Note that both of these are equivalent since $a_{n} = a_{1} + (n - 1) d$ $a_n = a_1 + (n- 1)d$ .

$S = \frac{3}{2} (22 + 4) = 39$ $S = 3/2 (22 + 4) = 39$ or $S = \frac{3}{2} (2 \cdot 22 - 9 \cdot 2) = 39 .$ $S = 3/2 ( 2\cdot 22 - 9\cdot 2) = 39.$

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What is the sum of the arithmetic sequence 22, 13, 4?

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