Question

If the first term of geometric progression g₁ , g₂ , g₃ , g₄ , .......... is unity, then the minimum value of 4g₂ + 5g₃ is equal to

(A) - 8/5

(B) - 2/5

(C) - 4/5

(D) -1/5

Answer 1

Correct Answer is: (C) - 4/5

 Let common ration of G.P. = r

Now, g₁ = 1, g₂ = r, g₃ = r²

∴ 5g₃ + 4 g₂ = 5r² + 4r

= 5[(r + 2/5)² - 4/25)] = 5(r + 2/5)² - 4/5

So, minimum value is - 4/5 occurs at r = - 2/5