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Find the sum of all natural numbers that are less than 100 and divisible by 4.
To do: The sum of all natural numbers that are less than 100 and divisible by 4
Solution:
The smallest natural number divisible by 4 is 4
The largest number within 100 which is divisible by 4 is 96
Thus, first term, a=4
Common difference is d=8-4=4
We will find the total number , n=?
$a_n=96$
$a_n=a+(n-1)d$
$96=4+(n-1)4$
$96-4=4n-4$
$92+4=4n$
$96=4n$
$n=\frac{96}{4}$
$n=24$
We can directly find n by directly multiplying $\frac{96}{4}$
Now,
$S_n=\frac{n}{2}\times (a+a_n)$
$S_n=\frac{24}{2}\times (4+96)$
$S_n=\frac{24}{2}\times 100$
$S_n= 12\times 100$
So when we do it,we get
$S_n=1200$
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