Choose two of the following choices that can represent the nth term of the sequence: 54, 18, 6, 2, ...
Accepted Solution
A:
Answer:The nth term of the given sequence is [tex]a_n = 54 \times (\frac{1}{3} )^{(n-1)}[/tex].Step-by-step explanation:Here, the first term of the sequence = 54Second term = 18Third term = 6Now, [tex]\frac{18}{56 } =\frac{1}{3} [/tex]and, [tex]\frac{6}{18 } = \frac{1}{3} [/tex]as [tex]\frac{a_2}{a_1} = \frac{a_3}{a_2} =\frac{1}{3} [/tex]Hence, the terms of the given sequence are in GEOMETRIC PROGRESSION with common ratio = 1/3Now, the nth term in GP is given as [tex]a_n = a r^{(n-1)}[/tex]So here, [tex]a_n = 54 \times (\frac{1}{3} )^{(n-1)}[/tex]Hence, nth term of the given sequence is [tex]a_n = 54 \times (\frac{1}{3} )^{(n-1)}[/tex].