If-the-G-M-between-two-numbers-a-b-is-G-and-the-two-A-M-s-between-them-are-p-and-q-then-prove-that-G-2-2p-q-2q-p-

Question Number 3617 by Rasheed Soomro last updated on 16/Dec/15

I f t h e G . M . b e t w e e n t w o n u m b e r s

a, b i s G a n d t h e t w o A . M .^{'} s b e t w e e n

t h e m a r e p a n d q, t h e n p r o v e t h a t

G^{2} = (2 p - q) (2 q - p) .

Commented by Yozzii last updated on 16/Dec/15

T h e r e a r e m u l t i p l e d e f i n i t i o n s o f t h e

A . M b e t w e e n a a n d b ?

Commented by prakash jain last updated on 16/Dec/15

AP : a, a + d, a + 2 d, b = a + 3 d

p = a + d, q = a + 2 d

2 p - q = 2 a + 2 d - a + 2 d = a

2 q - p = 2 (a + 2 d) - (a + d) = a + 3 d = b

(2 p - q) (2 q - p) = a b = G^{2}

Commented by prakash jain last updated on 16/Dec/15

n AM s x_{i} between a and b means

a, x_{1}, x_{2}, \dots, x_{n}, b is an AP .