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Arithmetic Progression Terms Relation

CAT 2017 Slot 1 · Quantitative Ability · Medium · Progressions

This is a medium Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Progressions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is:

  1. A.

    2 : 3

  2. B.

    3 : 2

  3. C.

    3 : 4

  4. D.

    4 : 3

Answer

A

Explanation

Let first term = aa, common difference = d>0d > 0. T7=a+6d,T3=a+2d,T17=a+16dT_7 = a + 6d, T_3 = a + 2d, T_{17} = a + 16d. Given: (a+6d)2=(a+2d)(a+16d)(a + 6d)^2 = (a + 2d)(a + 16d) a2+12ad+36d2=a2+18ad+32d2a^2 + 12ad + 36d^2 = a^2 + 18ad + 32d^2 4d2=6ad  ⟹  2d=3a  ⟹  ad=234d^2 = 6ad \implies 2d = 3a \implies \frac{a}{d} = \frac{2}{3}.

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