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


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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

	$l e t t w o n u m b e r i s p, q$ $g i v e n p, A, q [a r e i n A . P]$ $s o A - p = q - A \to 2 A = p + q . . . . . (1)$ $S i s s u m o f n a r i t h m a t i c m e a n$ $f i r s t t e r m = p + d$ $l a s t t e r m = q - d$ $S = \frac{n}{2} [p + d + q - d]$ $S = \frac{n}{2} \times 2 A$ $S = n A$
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