1.

Let A_1,A_2,A_3,….,A_m be the arithmetic means between -2 and 1027 and G_1,G_2,G_3,…., G_n be the gemetric means between 1 and 1024 .The product of gerometric means is 2^(45) and sum of arithmetic means is 1024 xx 171 The number 2 A_(171,G_5^2+1,2A_(121)

Answer»

A.P
G.P
H.P
none of these

Solution :We have
`A_(171)+A_(172)=-2+1027=1025`
or `(2A_(171)+2A_(172))/2=1025`
Also,
`G_(5)=1xx2^(5)=32`
`rArrG_(5)^(2)=1024`
or `G_(5)^(2)+1=1025`
HENCE, `2A_(171),G_(5)^(2)+1,2A_(172)` are in A.P.


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