Question

Warning :- "Only for geniuses"

Solve the question given in the attachment​

Answer 1

Answer:

Since a, an+bn/an-1+bn-1 and b are in A.P, we have

(a + b)/2 = (an+bn /an-1+bn-1) [AM between two numbers in AP]

(a + b)( an-1+bn-1) = 2 an + 2bn

an + ban-1+ abn-1 + bn = 2an + 2bn

ban-1+ abn-1 = an + bn

abn-1 – bn =  an – ban-1

bn-1( a – b) =  an-1( a – b)

bn-1 =  an-1

bn-1 / an-1 = 1

(b/a) n-1 = (b/a)0

On comparing both the sides, we get

n – 1 = 0

Therefore, n = 1