Question

What is the sum of the first 29 terms of the arithmetic sequence? −43,−35,−27,−19,... Enter your answer in the box. S29=

Answer 1

Answer: $S_{29}$ = 2001

Step-by-step explanation:

Since the sequence is an arithmetic sequence , it means that a common difference must exist.

Let the terms in the sequence be $T_{1}$ , $T_{2}$ , $T_{3}$ , $T_{4}$ , ...

Then common difference = $T_{2}$ - $T_{1}$ = $T_{3}$ - $T_{2}$ = 8

That is , the common difference (d) = 8

The formula for calculating sum of  n terms is given by :

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

Where ;

n = number of terms

a = first term

d = common difference

From the question :

n = 29

a = -43

d = 8

Substituting into the formula , we have

$S_{29}$ = $\frac{29}{2}$ [ 2{-43} + (29-1)(8) ]

$S_{29}$ = $\frac{29}{2}$ (-86 +224)

$S_{29}$ = $\frac{29}{2}$ ( 138)

$S_{29}$ = $\frac{4002}{2}$

$S_{29}$ = 2001