The-arithmetic-mean-between-two-numbers-is-A-and-S-is-the-sum-of-n-arithmetic-means-between-these-numbers-then-

Question Number 82540 by zainal tanjung last updated on 22/Feb/20

The arithmetic mean between two numbers

is A, and S is the sum of n arithmetic means

between these numbers, then

Answered by TANMAY PANACEA last updated on 22/Feb/20

l e t t w o n u m b e r i s p, q

g i v e n p, A, q [a r e i n A . P]

s o A - p = q - A \to 2 A = p + q \dots . . (1)

S i s s u m o f n a r i t h m a t i c m e a n

f i r s t t e r m = p + d

l a s t t e r m = q - d

S = \frac{n}{2} [p + d + q - d]

S = \frac{n}{2} \times 2 A

S = n A