Question

Let < a_n> be a G.P. such that and a₂ + a₅ = 216. Then

a₁ is equal to

• A. 12 or $\frac { 108 } { 7 }$
• B. 10
• C. 7 or $\frac { 54 } { 7 }$
• D. None of these

Answer 1

Answer: (A)

12 or $\frac { 108 } { 7 }$

Answer 2

Let the G.P. be a, ar, ar² , ……………….

$\frac { a _ { 4 } } { a _ { 6 } }$ = $\frac { 1 } { 4 } \Rightarrow$ r² = 4 ; r = 2, – 2

case-I : If r = 2

a₂ + a₅ = 216

ar + ar⁴ = 216

a₁ = 12, r = 2

case-II : r = – 2

a₂ + a₅ = 216

ar + ar⁴ = 216

a = $\frac { 216 } { 14 } = \frac { 108 } { 7 }$