Question

Choose two of the following choices that can represent the nth term of the sequence: 54, 18, 6, 2, ...

Answer 1

Answer:

The nth term of the given sequence is $a_n = 54 \times (\frac{1}{3} )^{(n-1)}$.

Step-by-step explanation:

Here, the first term of the sequence = 54

Second term = 18

Third term = 6

Now, $\frac{18}{56 } =\frac{1}{3}  $

and, $\frac{6}{18 } = \frac{1}{3}$

as $\frac{a_2}{a_1}  = \frac{a_3}{a_2}   =\frac{1}{3}$

Hence, the terms of the given sequence are in GEOMETRIC PROGRESSION with common ratio = 1/3

Now, the nth term in GP is given as $a_n = a r^{(n-1)}$

So here, $a_n = 54 \times (\frac{1}{3} )^{(n-1)}$

Hence, nth term of the given sequence is $a_n = 54 \times (\frac{1}{3} )^{(n-1)}$.