Theory of Intelligence
11TH•Mathematics•Sequences And Series•Question 17

Overview

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find number of terms.

First term (a=11). Let number of terms be (n), common difference (d).

Sum of first 4 terms: (\dfrac{4}{2}[2\cdot11+3d]=56\implies2(22+3d)=56\implies22+3d=28\implies d=2)

Last four terms: (a_{n-3}+a_{n-2}+a_{n-1}+a_n=112)

[ 4a+(4n-10)d=112 ] [ 4\cdot11+(4n-10)\cdot2=112 ] [ 44+8n-20=112 ] [ 8n+24=112\implies8n=88\implies n=11 ]

Answer: 11 terms

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