Question

n arithmetic means are inserted between the numbers 7 and 49. If the sum of these means be 364 then the sum their squares is –

• A. 10380
• B. 11380
• C. 11830
• D. 18130

Answer 1

Answer: (C)

11830

Answer 2

Q A₁ + A₂ + …..+A_n = n $\left( \frac{7 + 49}{2} \right)$ = 364

Ž n = 13

Hence 49 = 7 + 14d Ž d = 3

13 A.m’ s are given by 7 + 3k, k = 1, 2, 3……, 13

\ Desired sum = $\sum_{k = 1}^{13}{(7 + 3k)^{2}}$Ž 9$\sum_{k = 1}^{13}k^{2}$+ 42 $\sum_{k = 1}^{13}k$ + 49$\sum_{k = 1}^{13}{(1)}$= 11830.