Arithmetic Progression Terms Relation

CAT 2017 Slot 1 · QA · Medium · Progressions

All CAT 2017 Slot 1 questionsMore Progressions questionsAll CAT QA

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}.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace