Question

find the sum of three digit numbers from 100to 150

Answer 1

Answer:

The sum is 6375.

Step-by-step explanation:

Since, the numbers from 100 to 150 are,

100, 101, 102,........, 150

Which is an A.P.,

Having the first term, a = 100,

The common difference, d = 1,

Let the number of terms is n,

Thus, the last term = a + (n-1) d = 100 + ( n - 1) = 99 + n,

According to the question,

99 + n = 150 ⇒ n = 51,

Hence, the sum of the above A.P. is,

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

$=\frac{51}{2}[2\times 100+(51-1)]$

$=\frac{51}{2}[200+50]$

$=\frac{51}{2}\times 250$

$=51\times 125=6375$