How do you find the sum of the arithmetic sequence 2 + 5 + 8 + ... + 56?

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Answer 1 · 2018-04-18T13:27:55

$532$ $color(blue)(532)$

The sum of an arithmetic series is given as:

$S_{n} = \frac{n}{2} (2 a + (n - 1) d)$ $S_n=n/2(2a+(n-1)d)$

Where:

$a$ $bba$ is the first term, $d$ $bbd$ is the common difference and $n$ $bbn$ is the nth term.

The nth term is given as:

$a + (n - 1) d$ $a+(n-1)d$

We first find the common difference:

$5 - 2 = 8 - 5 = 3$ $5-2=8-5=3$

We now find the number of terms. We know the last term is $56$ $56$ and the first term is $2$ $2$ :

$:.$

$2+(n-1)*3=56$

$(n-1)*3=54$

$n=54/3+1=19$

$:.$

$S_19=19/2(2+(19-1)*3)=19/2(56)=color(blue)(532)$