If p-qth term of a G-P- is -a- and its p-qth term is -b- where a- b - then its pth term is

Let 'A' be first term and 'r' be the common ratio. We have, a=Ar^p+q 1, b=Ar^p q 1 ⇒ ab = A^2 × r^2p 2 ⇒√(ab)=Ar^p 1=p^th term ...

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Standard XIII

Mathematics

Geometric Progression

If p+qth term...

Question

If $(p + q)^{th}$ term of a G.P. is $^{'} a^{'}$ and its $(p - q)^{th}$ term is $^{'} b^{'}$ where $a, b \in R^{+}$ , then its $p^{th}$ term is

\sqrt{\frac{a^{3}}{b}}

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\sqrt{\frac{b^{3}}{a}}

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\sqrt{a b}

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None of these

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Solution

The correct option is C $\sqrt{a b}$
Let $^{'} A^{'}$ be first term and $^{'} r^{'}$ be the common ratio.
We have,
$a = A r^{p + q - 1}, b = A r^{p - q - 1}$
$\Rightarrow a b = A^{2} \times r^{2 p - 2}$
$\Rightarrow \sqrt{a b} = A r^{p - 1} = p^{th} term$

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Similar questions

Q. If

(p + q)^{th}

term of a G.P. is

^{'} a^{'}

and its

(p - q)^{th}

term is

^{'} b^{'}

where

a, b \in R^{+}

, then its

p^{th}

term is

Q. If

(p + q)^{th}

term of a G.P. is

^{'} a^{'}

and its

(p - q)^{th}

term is

^{'} b^{'}

where

a, b \in R^{+}

, then its

p^{th}

term is

If the $(p + q)^{t h}$ term of a G.P. is m and $(p - q)^{t h}$ term is n, then pth term will be _____.

If $(p + q)^{t h}$ and (p - q)th terms of a G.P. are m and n respectively, then write its pth term.

The first term of the G.P is 1 . If ${(p + q)}^{t h}$ term of G.P. is `a` and it's ${(p - q)}^{t h}$ term is `b` where a, b ∈ $R^{+}$ then it's $p^{t h}$ term is:

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Geometric Progression

Standard XIII Mathematics

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If (p+q)th term of a G.P. is ′a′ and its (p−q)th term is ′b′ where a, b∈R+, then its pth term is

The correct option is C √ab Let ′A′ be first term and ′r′ be the common ratio. We have, a=Arp+q−1, b=Arp−q−1 ⇒ab=A2×r2p−2 ⇒√ab=Arp−1=pth term

If $(p + q)^{th}$ term of a G.P. is $^{'} a^{'}$ and its $(p - q)^{th}$ term is $^{'} b^{'}$ where $a, b \in R^{+}$ , then its $p^{th}$ term is

The correct option is C $\sqrt{a b}$
Let $^{'} A^{'}$ be first term and $^{'} r^{'}$ be the common ratio.
We have,
$a = A r^{p + q - 1}, b = A r^{p - q - 1}$
$\Rightarrow a b = A^{2} \times r^{2 p - 2}$
$\Rightarrow \sqrt{a b} = A r^{p - 1} = p^{th} term$