An algebra problem by Ankit Nigam

Algebra Level 3

the sum of the first 100 terms common to the series 17, 21, 25, 29, 33.... and 16, 21, 26,31, 36..... is

110010 101100 111000 100101

Ankit Nigam by Ankit Nigam , 33, India

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1 solution

Sujoy Roy
Dec 7, 2014

First term and common difference of the given two series are 21 21 and 20 20 respectively. Sum of the first 100 100 terms of the new series is

S 100 = 100 2 [ 2 ∗ 21 + ( 100 − 1 ) ∗ 20 ] S_{100}=\frac{100}{2}[2*21+(100-1)*20] = 50 ∗ 2022 = 101100 =50*2022 = \boxed{101100}

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