Home » Past Questions » Mathematics » The fifth term in the progression \(9,27,81,{\dots}\) is

The fifth term in the progression \(9,27,81,{\dots}\) is


Question

The fifth term in the progression \(9,27,81,{\dots}\) is

Options

A) \(243\)

B) \(3^7\)

C) \(729\)

D) \(3^8\)

The correct answer is C.

Explanation:

If \(\cfrac{T_2}{T_1} = \cfrac{T_3}{T_2}\), the progression is a G.P.
If \(T_2 - T_1 = T_3 - T_2\), the progression is an A.P
Sine \(\frac{27}{9} = \frac{81}{27}\), the progression is a G.P.
\(r = \cfrac{27}{9} = 3\)
\(T_5 = ar^{n-1}\)
\(= 9 \times 3^{5-1}\)
\(= 3^2 \times 3^4\)
\(T_5 = 3^6\)

More Past Questions:


Dicussion (1)

  • If \(\cfrac{T_2}{T_1} = \cfrac{T_3}{T_2}\), the progression is a G.P.
    If \(T_2 - T_1 = T_3 - T_2\), the progression is an A.P
    Sine \(\frac{27}{9} = \frac{81}{27}\), the progression is a G.P.
    \(r = \cfrac{27}{9} = 3\)
    \(T_5 = ar^{n-1}\)
    \(= 9 \times 3^{5-1}\)
    \(= 3^2 \times 3^4\)
    \(T_5 = 3^6\)

    Reply
    Like