Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

12220

12250

13250

13235

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given:
The numbers between 1 and 500 that are the multiples are 2 as well as 5 are given below –
10,20,30,40,50,...,490
Since these numbers form an Arithmetic Progression (A.P.) series.
The first term of the series
a=10
The last term of the series
l=490
And the common difference between two consecutive terms
d=(20−10)d=10
Let us assume the number of the terms in this series is n .
To find the number of terms we use the formula for the nth term. So, we get,
The last term of the series,
l=a+(n−1)d
Substituting the values in the formula we get,
⇒490=10+(n−1)×10⇒480=(n−1)×10⇒48=n−1⇒n=49
So, there are 49 terms in this series.
Now we have all the values needed to calculate the sum of the series. So, the sum of the series by using the formula for the sum of the Arithmetic Progression (Sn) series is given by –
Sn=