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Standard X

Mathematics

nth Term of an AP

The first ter...

Question

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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√ab

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Solution

The correct option is C
√ab

$T_{P + Q}$ = $r^{p + q - 1}$ ,

$T_{p - q}$ = $r^{p - q - 1}$

⇒ $T_{P}$ = $\sqrt{r^{(p - 1)^{2}}}$

= $\sqrt{r^{p + q - 1} . r^{p - q - 1}}$

= $\sqrt{a b}$

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Similar questions

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:

Q. If

(p + q)^{th}

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^{'} a^{'}

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(p - q)^{th}

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^{'} b^{'}

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, then its

p^{th}

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Q. If

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^{'} a^{'}

and its

(p - q)^{th}

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^{'} b^{'}

where

a, b \in R^{+}

, then its

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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 _____.

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The first term of the G.P is 1 . If (p+q)th term of G.P. is `a` and it's (p−q)th term is `b` where a, b ∈ R+ then it's pth term is:

The correct option is C √ab TP+Q = rp+q−1, Tp−q = rp−q−1 ⇒ TP = √r(p−1)2 = √rp+q−1.rp−q−1 = √ab

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:

The correct option is C
√ab

$T_{P + Q}$ = $r^{p + q - 1}$ ,

$T_{p - q}$ = $r^{p - q - 1}$

⇒ $T_{P}$ = $\sqrt{r^{(p - 1)^{2}}}$

= $\sqrt{r^{p + q - 1} . r^{p - q - 1}}$

= $\sqrt{a b}$