Question

If the first and the nth terms of a G.P. are a and b

respectively and if P is the product of the first n

terms, prove that

2

( )n P ab  .​

Answer 1

Given:-

first term = a

last  term = b = $t_{n}$

To prove :-

$p^{2} = ab^{n}$

solution:-

$t_{n} = a = r^{n-1} = b$

= $r = ( \frac{b}{a} )^{\frac{1}{n} - 1 }$

product of $n^{th}$

$p = a_{1} ,a_{2}, ....... a_{n}$

$= a, ar^{1} , ar^{2} ...... ar^{n-1}$

$p = a^{n} r^{n(n-1)/2}$

$p^{2} = a^{2} (r^{n-1} )^n$

$p^{2} = a , r^{n-1}$

$p^{2} = (ab)^{n}$

hence prove