Question

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

Solution

## Clearly, the first seven numbers which are multiples of 2, as well as 9, are $$18,36,54.....126.$$This is an AP with first term $$a=18$$ and last term $$l=126$$. Let $$S_n$$ be the sum of n terms of an AP. Then, $$S_n=\cfrac n2(a+l)$$Putting $$a=18,n=7$$ and $$l=126$$ in $$S_n$$, we get$$S_7=\cfrac 72(18+126) \Rightarrow S_7=\cfrac 72(144) \Rightarrow S_7=504$$Mathematics

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