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Find the sum of the first seven numbers which are multiples of 2 as well as of 9. [Hint: Take the LCM of 2 and 9]

Solution:

Given, the series is a multiple of 2 as well as 9.

Also, take the LCM of 2 and 9.

We have to find the sum of the first seven numbers.

LCM of 2 and 9 is 18.

So, the series is a multiple of 18.

The first seven multiple of 18 are (18×1), (18×2), (18×3), (18×4), (18×5), (18×6), (18×7)

Therefore, the series is 18, 36, 54, 72, 90, 108, 126.

If l is the last term of an AP, then the sum of the terms is given by

S = n/2[a+l]

Here, first term, a = 18

Last term, l = 126

Common difference, d = 18

S = 7/2[18 + 126]

= 7/2[144]

= 7(72)

= 504

Therefore, the sum of the first seven numbers which are multiples of 2 as well as 9 is 504.

✦ Try This: Find the sum of the first seven numbers which are multiples of 3 as well as of 7. [Hint: Take the LCM of 3 and 7]

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 31

Find the sum of the first seven numbers which are multiples of 2 as well as of 9

Summary:

The sum of the first seven numbers which are multiples of 2 as well as of 9 [Hint: Take the LCM of 2 and 9] is 504

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