Question

Find the sum of all positive integers, from 5 to 1555 inclusive, that are divisible by 5

Answer 1

all the multiple of five will for an ap
with first term 5
last term 1555
common diffrence=5
and number of terms =1555÷5=311
so sum of all terms =311(5+1555)/2=242580

Answer 2

Answer:

242580

Step-by-step explanation:

Given : Positive integers from 5 to 1555 inclusive

To Find :Find the sum of all positive integers, from 5 to 1555 inclusive, that are divisible by 5

Solution:

All positive integers, from 5 to 1555 inclusive, that are divisible by 5:

5,10,15,.......,1555

It forma an AP

a = first term = 5

d = common difference = 10-5=15-10 =5

Formula of nth term : $a_n=a+(n-1)d$

$1555=5+(n-1)5$

$1555-5=(n-1)5$

$1550=(n-1)5$

$\frac{1550}{5}=(n-1)$

$310=(n-1)$

$310+1=n$

$311=n$

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

Substitute n = 311

$S_n{311}=\frac{311}{2}(2(5)+(311-1)5)$

$S_n{311}=242580$

Hence the sum of all positive integers, from 5 to 1555 inclusive, that are divisible by 5 is 242580