QJEEM19Mabb7c: JEE Main 2019 Mathematics - Class 11 JEEM19Mabb7c Solution: Let a, b and c be the 7 th , 11 th and 13 th terms respectively …

Question

Verified Solution • 2025–26 Session moderate

Let a, b and c be the 7^th, 11^th and 13^th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then

\frac{a}{c}

equal to :

Accepted Answer

T₇ = A + 6d = a; T₁₁ = A + 10d = b; T₁₃ = A + 12d = c

Now a, b, c are in G.P.

∴

b² = ac

\Rightarrow

(A + 10d)² = (A + 6d) (A + 12d)

\Rightarrow

A² + 100d² + 20Ad = A² + 18Ad + 72d²

\Rightarrow

A + 14d = 0, A =

-

14d

\frac{a}{c} = \frac{A + 6 d}{A + 12 d} = \frac{- 8 d}{- 2 d} = 4

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