Question 72

What will be the average of 16, 17, 18, ..... upto fifteen terms?

Solution

Sum of the terms in the series = $$\dfrac{n}{2}\times [2a+(n-1)d]$$
where n = number of terms, a = first term, d = difference between any two terms.
Sum of the terms = $$\dfrac{15}{2}\times [2\times16+(15-1)1] = \dfrac{15}{2}\times(32+14) = \dfrac{15}{2}\times46 = 15\times23 = 345$$
Average $$= \dfrac{345}{15} = 23$$


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