Question
If (p+q)th term and (p−q)th term of a G.P. be m and n, then the pth term will be ___.
Answer: Option B
:
B
Given that
ap+q=arp+q−1=m and ap−q=arp−q−1=n.
⇒m×n=arp+q−1 x arp−q−1
=a2r2(p−1)
=(arp−1)2
⇒√mn=arp−1=ap
Thus, the pth term of the GP is√mn.
Aliter: Each term in a G.P. is the geometric mean of the terms equidistant from it. Here, (p+q)th and (p−q)th terms are equidistant from the pth term.
∴ pth term(√mn) will be G.M. of (p+q)th and (p−q)th terms.
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:
B
Given that
ap+q=arp+q−1=m and ap−q=arp−q−1=n.
⇒m×n=arp+q−1 x arp−q−1
=a2r2(p−1)
=(arp−1)2
⇒√mn=arp−1=ap
Thus, the pth term of the GP is√mn.
Aliter: Each term in a G.P. is the geometric mean of the terms equidistant from it. Here, (p+q)th and (p−q)th terms are equidistant from the pth term.
∴ pth term(√mn) will be G.M. of (p+q)th and (p−q)th terms.
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