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Question

Prathyusha stated that "the average of first 10 odd numbers is also 10". Do you agree with her? Justify your answer.

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Solution

First 10 odd numbers-
1,3,5,7,9,11,13,15,17,19
The above series forms an A.P. with first term and common difference of 1 and 2.
As we know that sum of n terms in an A.P. is given as-
Sn=n2(a+l)
Whereas, a and l are first and last term.
Sum of first 10 odd numbers-
S10=102(1+19)
S10=5×20=100
Now, average of first 10 odd numbers-
Av. =Snn=10010=10
Thus the average of first 10 odd numbers is 10.
Hence I agree with Pratyusha as the average of first 10 odd numbers is 10.

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