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

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)` =
`(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)` =
`(29)/(2)` [ 2{-43} + (29-1)(8) ]

`S_(29)` =
`(29)/(2)` (-86 +224)

`S_(29)` =
`(29)/(2)` ( 138)

`S_(29)` =
`(4002)/(2)`

`S_(29)` = 2001