If 2nd term of a G.P is 24 and 5th term is 81, then first term is A)

1.	If 2nd term of a G.P is 24 and 5th term is 81, then first term is A) 16B) 20 C) 3/2D) 3
Answer» 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. Correct option is A) 16

If 2nd term of a G.P is 24 and 5th term is 81, then first term is A) 16B) 20 C) 3/2D) 3

Answer»

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.

Correct option is A) 16