How do you find $S_n$ for the arithmetic series given d=5, n=16, $a_n=72$ ?

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Answer 1 · 2017-05-15T10:50:04

$S_n=552$

$d=5 , n=16 ,a_n=a_16=72 , a_1= ? , S_n=S_16= ?$

We know $a_n= a_1+ (n-1)*d ; :. 72 = a_1+ (16-1) *5$ or
$a_1= 72-75 = -3$

We know $S_n= n/2 {2a_1+ (n-1)*d} :. S_16= 16/2 {2*(-3)+ (16-1)*5}$ or
$S_16= 8 *{-6+ 75} or S_16= 8 * 69 = 552$

$S_n=552$ [Ans]

How do you find S_nS_n for the arithmetic series given d=5, n=16, a_n=72a_n=72?