If p-q th term of G-P- is m and p-qth term is n- then pth term will beA- m - n B- m - n C- mnD- - mn

The correct option is D √(mn) T_p+q=ar^p+q 1=m ....................(1) T_p q=ar^p q 1=n .......................(2) T_p=ar^p 1 ........................ ...

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Standard XII

Mathematics

Geometric Progression

If p+q th ter...

Question

If (p+q)th term of G.P. is m and (p-q)th term is n, then pth term will be

$(\frac{m}{n})$

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$(m - n)$

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$m n$

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$\sqrt{m n}$

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Solution

The correct option is D
$\sqrt{m n}$

$T_{p + q} = a r^{p + q - 1} = m . . . . . . . . . . . . . . . . . . . . (1) T_{p - q} = a r^{p - q - 1} = n . . . . . . . . . . . . . . . . . . . . . . . (2) T_{p} = a r^{p - 1} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)$
Multiplying (1) and (2)
$a^{2} r^{2 p - 2} = m n \Rightarrow T_{p} = a r^{p - 1} = \sqrt{m n}$

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If (p+q)th term of G.P. is m and (p-q)th term is n, then pth term will be

The correct option is D √mn Tp+q=arp+q−1=m....................(1) Tp−q=arp−q−1=n.......................(2) Tp=arp−1.....................................(3) Multiplying (1) and (2) a2r2p−2=mn⇒Tp=arp−1=√mn