The third term of a G.P. is 42. Find the product of its first five terms.

Question

The third term of a G.P. is 42. Find the product of its first five terms. (A) 42 (B) (42)5 (C) 98 (D) (25)5

Tardigrade Admin · Accepted Answer

Let a be the first term and r be the common ratio. Then, a3 = 42 ⇒ ar2 = 42 ...(i) ∴ Product of first five terms = a1a2a3a4a5 = a(ar)(ar2)(ar3)(ar4) = a5r10 = (ar2)5 = (42)5 [Using (i)]

Q. The third term of a $G . P$ . is $42$ . Find the product of its first five terms.

$42$

$(42)^{5}$

$98$

$(25)^{5}$

Let $a$ be the first term and $r$ be the common ratio. Then, $a_{3} = 42$
$\Rightarrow a r^{2} = 42 ... (i)$
$∴$ Product of first five terms $= a_{1} a_{2} a_{3} a_{4} a_{5}$
$= a (a r) (a r^{2}) (a r^{3}) (a r^{4})$
$= a^{5} r^{10}$
$= (a r^{2})^{5}$
$= (42)^{5}$ [Using $(i)$ ]

Q. The third term of a G.P. is 42. Find the product of its first five terms.

42

(42)5

98

(25)5