Question

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

Answer 1

The nth term of the given sequence is
`a_n = 54 * ((1)/(3) )^((n-1))`.

Explanation:

Here, the first term of the sequence = 54

Second term = 18

Third term = 6

Now,
`(18)/(56 ) =(1)/(3)`

and,
`(6)/(18 ) = (1)/(3)`

as
`(a_2)/(a_1)  = (a_3)/(a_2)   =(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 * ((1)/(3) )^((n-1))`

Hence, nth term of the given sequence is
`a_n = 54 * ((1)/(3) )^((n-1))`.