Question Bank - Mathematics

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What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ?

A.
50
B.
51
C.
100
D.
102

Solution:

Formula used:Sum of n terms of AP = \(\frac{n}{2}[2a + (n-1)d]\)Where a and d are the first term & common differences of AP.Arithmetic mean = (Sum of all terms)/Total number of termsCalculation:Given that, for an APa = 4, d = 4 & n = 4Using the formula of the sum of APS = \(\frac{n}{2}[2a + (n-1)d]\)? S = \(\frac{50}{2}[2× 4+ (50-1)4]\)? S = 25(8 + 196) = 25 × 204Now, arithmetic mean of 50 terms isA = \(\frac{25\times 204}{50}\) = 102? The required arithmetic mean is 102.

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