If 2nd term of a G.P is 24 and 5th term is 81, then first term is
If 2nd term of a G.P is 24 and 5th term is 81, then first term is
A) 16
B) 20
C) 3/2
D) 3
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Correct option is (A) 16
In G.P., \(a_2=24\;\&\;a_5=81\)
Let first term and common difference of G.P. be a and r.
\(\therefore ar=24\) ______________(1) \((\because a_2=ar)\)
and \(ar^4=81\) ______________(2) \((\because a_5=ar^4)\)
Divide equation (2) by (1), we get
\(\frac{ar^4}{ar}=\frac{81}{24}\)
\(\Rightarrow r^3=\frac{27}8\)
\(=\frac{3^3}{2^3}=(\frac32)^3\)
\(\Rightarrow\) \(r=\frac32\)
Put \(r=\frac32\) in equation (1), we get
\(\frac32a=24\)
\(\Rightarrow a=24\times\frac23=16\)
Hence, first term of G.P. is 16.
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