Question

1. Find the sum of the first 150 counting numbers.​

Answer 1

Answer:

first 150 counting numbers are 1,2,3,4,....,150

here,

1, 2, 3 ,..., 150 forms AP with a = 1 and d = 1

$sum \: of \: all \: terms \: of \: ap \\ = \frac{n}{2} (2a \: + (n - 1)d \: )$

$sum \: of \: all \: terms \: of \: ap \\ = \frac{150}{2} (2 \times 1 \: + (150 - 1)1 \: )$

$sum \: of \: all \: terms \: of \: ap \\ = 75 (2 + (149))$

$sum \: of \: all \: terms \: of \: ap \\ = 75 (151)$

Sum of first 150 counting numbers is 11325

Answer 2

Given:

Find the sum of the first 150 counting numbers.​

Solution:

Know that the sum of the first $n$ natural numbers is given as,

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

Therefore the sum of the first 150 counting numbers is -

$\[ = \frac{{150\left( {150 + 1} \right)}}{2}\]$

$\[ = \frac{{150 \times 151}}{2}\]$

$\[\begin{array}{l} = 75 \times 151\\ = 11325\end{array}\]$

Hence, the sum of the first 150 counting numbers is 11325.