IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 13 : Let S_n be sum of the first n terms of an A.P. {a_n }. If S₅ = S₉ , what is the ratio of a₃ : a₅

1. 9:5
2. 5:9
3. 3:5
4. 5:3

Video Explanation

Explanatory Answer

Let S_n be the sum of the first n terms of an A.P.
It is given that S₅ = S₉
a₁ + a₂ + a₃ +a₄ + a₅ = a₁ + a₂ + a₃ +a₄ + a₅ + a₆ + a₇ + a₈ + a₉
 a₆ + a₇ + a₈ + a₉ = 0
Let us suppose ‘a’ be the middle term of the a₇ and a₈
And let us supposea₈ - a₇ = 2d than a - a₇ = d and a₈ - a = d
a₇ = a - d, a₈ = a + d
a₆ = a - 3d and a₉ = a + 3d
We know that a₆ + a₇ + a₈ + a₉ = 0. If we substitute the above values, we will get
a = 0
So that, the values of a₁ , a₂ , a₃ , a₄ , a₅ , a₆ , a₇ , a₈ , a₉ becomes -13d, -11d, -9d, -7d, -5d, -3d, -d, d, 3d
Hence a₃ : a₅ = 9 : 5

The question is " Let S_n be sum of the first n terms of an A.P. {a_n }. If S₅ = S₉ , what is the ratio of a₃ : a₅ "

Hence, the answer is '9:5'

Choice A is the correct answer.

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