Question

Find the sum of the series to $30$ terms:
$1-50+4-45+7-40+$ ...

• A. $-945$
• B. $105$
• C. $945$
• D. $1605$

Answer 1

The correct option is B $105$

Here the Series is $=(1-50)+(4-45)+(7-40)+...\left(30terms\right)$

$=-49-41-\mathrm{33....}\left(15terms\right)$

Difference $d=-41-(-49)=-33-(-41)=8$

Sum, $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

Since the series is made by combining two terms (i.e, $(1-50),(4-45)$...) therefore we will have to take the sum of the first $15$ terms for the newly formed series to get the sum of first $30$ terms of the given series.

$\therefore S_{15}=\frac{15}{2}[2\times (-49)+(15-1)\left(8\right)]=105$