How do you find the sum of the arithmetic sequence given 26+19+12+5+....(-37)?

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Answer 1 · 2016-05-26T15:17:30

The sum of the arithmetic sequence $=-55$

The arithmetic sequence provided is :
$26 + 19 + 12 + 5 + ......-37$

The first term: $a_1 = 26$
The common difference for the sequence can be found as follows:
$a_2 - a_1 = 19 - 26 =-7$
$color(blue)(d =-7$
The last term $a_n = -37$

We can find the total number of terms $(n)$ of the series by using the formula:
$color(blue)(a_n = a_1 + ( n-1)d$

$-37 = 26 + ( n-1) xx color(blue)((-7))$

$-37 = 26 -7n + 7$

$-37 = 33-7n$

$7n = 33 + 37$

$7n = 70$

$n = 10$

Now we find the sum of the terms applying the below mentioned formula:

$color(green)(S_n = n/2 (a_1 + a _n)$

$=10/2 ( 26 +(-37))$

$=5 xx (-11)$

$=-55$