Question

The maximum sum of the A.P. 40, 38, 36, 34,….is

• A. 390
• B. 420
• C. 460
• D. None of these

Answer 1

Answer: (B)

420

Answer 2

Let nth term be the first negative term.

T_n < 0

40 + (n – 1) – 2 < 0 or 42 – 2n < 0

2n > 42 or n > 21

Hence first 21 terms of A.P are non -negative

sum will be maximum if no negative terms is taken.

S_max = $\frac { 21 } { 2 }$[2 × 40 + 20 (– 2)] = 420