If frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}} be A.M. of a and b , then n=

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8. Sequences and Series

easy

If $\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}$ be the $A.M.$ of $a$ and $b$, then $n=$

A

$1$

B

$- 1$

C

$0$

D

None of these

Solution

(c) $\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}} = \frac{{a + b}}{2}$

$ \Rightarrow $ ${a^{n + 1}} – a{b^n} + {b^{n + 1}} – b{a^n} = 0$

$ \Rightarrow $$(a – b)({a^n} – {b^n}) = 0$

If ${a^n} – {b^n} = 0$.

Then ${\left( {\frac{a}{b}} \right)^n} = 1 = {\left( {\frac{a}{b}} \right)^0}$.

Hence $n = 0$.

Standard 11

Mathematics

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