Question

Q 6

Answer 1

For a G.P.,
First term = a
Let the common ratio = r
n^th term = b
⇒ ar^n-1 = b
P = Product of first n number of the given G.P.
⇒ P = a x ar x ar² x ar³ x.............x ar^n-1
⇒ P = a x ar x ar² x ar³ x.............x b

⇒ P = a x ar x ar² x ar³ x.............x `"b"/"r"^2xx"b"/"r"xx"b"`

⇒ P = (ab) x `("ar" xx "b"/"r")xx("ar"^2xx"b"/"r"^2)xx`............`"n"/2` terms

⇒ P = (ab) x (ab) x (ab) x.............`"n"/2` terms

⇒ P = `("ab")^("n"/2)`

⇒ P = `sqrt("ab"^"n")`

⇒ P² = `"ab"^"n"`