Question 54

How many multiples of 3 are there among the integers 15 to 105 inclusive?

Solution

Multiples of 3 are : 15,18,21,.....,102,105

The above series is an A.P. with first term = $$a=15$$ and common difference = $$d=3$$ and last term = $$l=105$$

Let number of terms be $$n$$

=> Number of terms = $$l=a+(n-1)d$$

=> $$15+(n-1)3=105$$

=> $$(n-1)3=105-15=90$$

=> $$n-1=\frac{90}{3}=30$$

=> $$n=31$$

=> Ans - (B)

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