Question

Find the sum of all natural numbers lying between 153 and 436 divisible by 8.

Answer 1

Between $153$ and $436$

number divisible by $8$ are $160,168,176,.....,432$

Let Total number are $n$

$\Rightarrow T_n=432,nth$ term of $A.P.$

(number are forming an $A.P.$)

$\Rightarrow T_n=a+(n-1)d$

$a=160,d=8$

$\Rightarrow 432=160+(n-1)8$

dividing by $8$

$54=20+(n-1)$

$\Rightarrow n-1=34$

$\Rightarrow n=35$

Name sum of these $35$ numbers.

$=S=\frac{35}{2}[160+432]$

using $S=\frac{n}{2}[a+l]$

$l=$ last term

$=\frac{35}{2}\left(592\right)$

$=10360$

$\Rightarrow Sum=10360$