# Find the Sum of the Following Serie: 101 + 99 + 97 + ... + 47 - Mathematics

Find the sum of the following serie:

101 + 99 + 97 + ... + 47

#### Solution

101 + 99 + 97 + ... + 47
Here, the series is an A.P. where we have the following:

$a = 101$

$d = \left( 99 - 101 \right) = - 2$

$a_n = 47$

$\Rightarrow 101 + (n - 1)( - 2) = 47$

$\Rightarrow 101 - 2n + 2 = 47$

$\Rightarrow 2n - 2 = 54$

$\Rightarrow 2n = 56$

$\Rightarrow n = 28$

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

$\Rightarrow S_{28} = \frac{28}{2}\left[ 2 \times 101 + \left( 28 - 1 \right) \times ( - 2) \right]$

$= \frac{28}{2}\left[ 2 \times 101 + 27 \times ( - 2) \right]$

$= 2072$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.4 | Q 2.2 | Page 30

Share