Q15 of 97 Page 185

If is the A.M. between a and b, then find the value of n.

A.M. of a and b =


Given, is the A.M. between a and b.


∴


⇒ (a + b) (an-1+ bn-1) = 2an + 2bn


⇒ an + abn-1 + ban-1 + bn = 2an + 2bn


⇒ abn-1 + ban-1 = an + bn


⇒ abn-1 – bn = an – ban-1


⇒ bn-1 (a – b) = an-1 (a – b)


⇒


⇒


⇒ n – 1 = 0


∴ n = 1


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