First slide

Arithmetic progression

Question

How many terms are to be added to make the sum 52 in the series $(- 8) + (- 6) + (- 4) + ...$ ?

Moderate

A

13
B

15
C

14
D

16

Solution

$S_{n} = 52 \Rightarrow \frac{n}{2} [2 (- 8) + (n - 1) 2] = 52$
$\begin{array}{l} \Rightarrow n (2 n - 18) = 104 \\ \Rightarrow n (n - 9) = 52 \Rightarrow n = 13 \end{array}$

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