Question

Find sum of all mo. B/w 250 ans 1000 divisible by 3

Answer 1

Answer:

156375

Step-by-step explanation:

We have to find the sum of all numbers between 250 and 1000 which are divisible by 3.

The first number divisible by 3 after 250 is 252.

The last number divisible by 3 before 1000 is 999.

So, the series goes  like this,

252 + 255 + 258 + ....+  999

Here the numbers are in Arithmetic Progression, with first term (a)=252

Common Difference (d) = 3

Last term (Tn) = 999

∴ We have to find the total number of terms in the given series.

$Tn = a + (n-1) \times d$

$999 = 252 + (n-1) \times 3$

$999 = 249 + 3 \times n$

∴$n = 250$

Now, we have to find the sum of all the numbers;

∵ $Sn = \frac{n}{2} \times (a+l)$

$\frac{250}{2} \times (252+999)$

$125 \times 1251$

156375

∴ The total sum of the series is 156375