How do you find the sum of the arithmetic sequence given d= -4, an = 27, and n = 9?

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Answer 1 · 2016-05-25T16:15:32

The sum of the terms of the progression:
$=color(blue)( 387$

The common difference: $d =- 4$

The/ last term: $a_n = 27$

The number of terms: $n =9$

Applying the formula:
$color(blue)(a_n = a_1 + (n-1)d$ , we can obtain the first term $(a_1)$ of the series.

$27 = a_1 + (9-1) xx (-4)$

$27 = a_1 + (8) xx (-4)$

$27 = a_1 -32$

$a_1 = 27 + 32$

$a_1 = 59$

Now, we calculate the sum using formula:
$color(green)(S_n = n/2 (a_1 + a_n)$

$S_n = 9/2 ( 59 + 27)$

$S_n = 9/2 ( 86)$

$S_n = 9/cancel2 ( cancel86)$

$S_n = 9 * 43$

$S_n = 387$