Question

Find the sum of numbers lying between 200 and 700 which are multiples of 5

Answer 1

Your answer

a=205

l=695

d=5

695=205+(n-1)5

490/5=n-1

n=99

sn=99/2(2*205+98*5)

sn=9306

Answer 2

Answer:

The sum is 44550  

Step-by-step explanation:

Given two numbers 200 and 700

we have to find the sum of numbers lying between 200 and 700 which are multiples of 5.

Multiples of 5 between 200 and 700 forms an A.P

$205, 210, 215, 220, 225, 230, .....695$

Common difference=d=210-205=5

first term, a=205

By recursive formula

$a_n=a+(n-1)d$

$695=205+(n-1)5$

$695-205=(n-1)5$

$490=(n-1)5$

$n-1=\frac{490}{5}=98$

$n=98+1=99$

Now, we have to find the sum of above A.P series by the formula

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

$S_{99}=\frac{99}{2}(2(205)+(99-1)5)$

$S_{99}=\frac{99}{2}(410+490)=\frac{99}{2}\times 900=44550$

Hence, the sum is 44550