Assertion -In a G-P- if the m - nth term be p and m - nth term be q- then its mth term is -pq- Reason- Tm-n- Tm- Tm - n are in G-P-

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Assertion :In a G.P. if the $(m + n)^{t h}$ term be p and $(m - n)^{t h}$ term be q, then its $m^{t h}$ term is $\sqrt{p q}$ . Reason: $T_{m + n}, T_{m}, T_{m - n}$ are in G.P.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Statement 2 is true as it is a property of sequence in G.P.

Now, $T_{m - n}, T_{m + n}$ are in G.P. ( $∵ T_{m}$ from $T_{m - n}$ and $T_{m + n}$ from $T_{m}$ are at same distance)

$∴ T_{m}^{2} = T_{m - n} T_{m + n}$

$\Rightarrow T_{m} = \sqrt{p q}$

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Assertion :In a G.P. if the (m+n)th term be p and (m−n)th term be q, then its mth term is √pq. Reason: Tm+n, Tm, Tm−n are in G.P.

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionStatement 2 is true as it is a property of sequence in G.P. Now, Tm−n,Tm+n are in G.P. (∵ Tm from Tm−n and Tm+n from Tm are at same distance)∴ T2m=Tm−nTm+n⇒ Tm=√pq

Assertion :In a G.P. if the $(m + n)^{t h}$ term be p and $(m - n)^{t h}$ term be q, then its $m^{t h}$ term is $\sqrt{p q}$ . Reason: $T_{m + n}, T_{m}, T_{m - n}$ are in G.P.