First slide

Introduction to statistics

Question

If the average of the numbers 148, 146, 144, 142, ... in AP, be 125, then the total numbers in the series will be

Easy

A

18
B

24
C

30
D

48

Solution

Given series is 148, 146, 144, 142, ... whose first term and common difference is
$\begin{array}{l} a = 148, d = (146 - 148) = - 2 \\ S_{n} = \frac{n}{2} [2 a + (n - 1) d] = 125 n (given) \\ \Rightarrow 125 n = \frac{n}{2} [2 \times 148 + (n - 1) \times (- 2)] \\ \Rightarrow n^{2} - 24 n = 0 \\ \Rightarrow n (n - 24) = 0 \Rightarrow n = 24 (n \neq 0) \end{array}$

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