Theory of Intelligence
11TH•Mathematics•Sequences And Series•Question 11

Overview

The 5th term of an arithmetic progression is 21 and the sum of first six terms is 90. Find the 18th term.

(a_5=21), (S_6=90)

[ a+4d=21\tag{1} ] [ \dfrac{6}{2}[2a+5d]=90\implies 3(2a+5d)=90\implies 2a+5d=30\tag{2} ]

From (1): (a=21-4d). Into (2): [ 2(21-4d)+5d=30\implies42-8d+5d=30\implies42-3d=30\implies3d=12\implies d=4 ] [ a=21-16=5 ]

[ a_{18}=5+17\cdot4=5+68=73 ]

Answer: (73)

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