Question 103

The average of all the odd integers between 2 and 22 is

Solution

Odd integers between 2 and 22 = 3, 5, 7,......, 21

This is an A.P. with first term = $$a=3$$ and $$d=2$$

Let number of terms = $$n$$

=> Last term = $$a+(n-1)d$$

=> $$3+(n-1)2=21$$

=> $$(n-1)2=21-3=18$$

=> $$(n-1)=\frac{18}{2}=9$$

=> $$n=9+1=10$$

Sum of series = $$\frac{n}{2}(a+l)$$

= $$\frac{10}{2}(3+21)$$

= $$5\times24=120$$

$$\therefore$$ Average = $$\frac{120}{10}=12$$

=> Ans - (D)

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