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Question

If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18,... are the same, find the value of n.

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Solution

Clearly 9,7,5,... is an AP with first term a=9 and common difference d=2 and 24,21,18,.... is an AP with first term A=24 and common difference D=3.
LetanandAn be the nth term of first and second AP respectively.
Therefore according to question,
an=An
a+(n1)d=A+(n1)D
9+(n1)×2=24+(n1)×3
2n+11=3n+27
n=16


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