Question

What is the sum of the first 34 numbers in the series below? 147 + 130 + 113 + 96 + . . .

Answer 1

-4,539

Explanation:

Given series is: 147 + 130 + 113 + 96 + . . .

Where first term a = 147

Common Difference d = 130 - 147 = - 17

No. of terms n = 34

To find:
`S_(34)`

By sum of n terms of an Arithmetic Progression, we have:

`S_(n)=(n)/(2)[2a + (n-1)d]`

Plugging the values of a, d and n in the above equation, we find:

`S_(34)=(34)/(2)[2(147) + (34-1)(-17)]`

`\therefore S_(34)=17[294 + (33)(-17)]`

`\therefore S_(34)=17[294 - 561]`

`\therefore S_(34)=17[-267]`

`\therefore S_(34)=-4,539`