First term of a G.P. of n terms is a and the last term l The product of all the terms of the G.P. is

Question

First term of a G.P. of n terms is a and the last term l The product of all the terms of the G.P. is (A) (n/2)(a+b) (B) (a+b)(n/2) (C) (al)(n/2) (D) (al)n

Tardigrade Admin · Accepted Answer

Product = (a)(ar) ........(arn-1) = anr1+2+.......+(n-1) = an r(n-1/2)(1+n-1) = an rn((n-1/2)) = (a2rn-1)n/ 2 = (al)n/ 2

Q. First term of a G.P. of n terms is a and the last term $l$ The product of all the terms of the G.P. is

$\frac{n}{2} (a + b)$

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

$(a l)^{\frac{n}{2}}$

$(a l)^{n}$

Product $= (a) (a r) ........ (a r^{n - 1})$
$= a^{n} r^{1 + 2 + ....... + (n - 1)} = a^{n} r^{\frac{n - 1}{2} (1 + n - 1)}$
$= a^{n} r^{n (\frac{n - 1}{2})}$
$= (a^{2} r^{n - 1})^{n /2}$
$= (a l)^{n /2}$

Q. First term of a G.P. of n terms is a and the last term l The product of all the terms of the G.P. is

2n​(a+b)

(a+b)2n​

(al)2n​

(al)n