- One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.
In this question we have been asked to Find the sum of all integers from 1 to 500 which are multiples of 2 as well as of 5.
CBSE DHANPAT RAI publications
CBSE Mathematics Class 10th
Question 55(iv)
First term(a) = 10, common difference(d) = 20 – 10 = 10 and nth term(an) = 500.
By using the formula of nth term of an A.P.
an = a + (n – 1)d
So,
=> 500 = 10 + (n – 1)10
=> 10(n – 1) = 490
=> n – 1 = 49
=> n = 50
Now by using the formula of sum of n terms of an A.P.
Sn = n[a + an] / 2
So,
S50 = 50[10 + 500]/2
= 25[510]
= 12750
Hence, sum of all integers from 1 to 500 which are multiples of 2 as well as of 5 is 12750.