Question

If the sixth term of an A.P. is equal to 2 ; the value of the common difference of A.P. which makes the product a₁ a₄ a₅ the greatest is (the i^th term denoted by a_i) –

• A. 8/5
• B. 3
• C. 2
• D. 4/5

Answer 1

Answer: (A)

8/5

Answer 2

a₁ + 5x = 2

̃ a₁ = 2 – 5x

now a₁.a₄.a₅ = (2 – 5x) (2 – 5x + 3x) (2 – 5x + 4x)

= (2 – 5x) (2 – 2x) (2 – x)

= 8 – 12x + 4x² – 20 x + 30 x² – 10x³

p = 8 – 32x + 34x² – 10x³

$\frac{dp}{dx}$ = – 32 + 68 x – 30x² = 0

x = $\frac{2}{3}$, $\frac{8}{5}$

$\frac{d^{2}p}{dx^{2}}$ = 68 – 60 x

for x = $\frac{8}{5}$, $\frac{d^{2}p}{dx^{2}}$ < 0

\ common diff. = 8/5