Question

What is the answer for this?​

Answer 1

The general formula for nth term of given sequence is:

`G_n = 54 . ((1)/(3))^(n-1)`

Explanation:

Given sequence is:

54,18,6.....

In order to write the general formula of a sequence, first of all the common ratio has to be found. Common ratio is the ratio between consecutive terms of a geometric sequence.

`Here\\a_1 = 54\\a_2 = 18\\a_3 = 6\\And\\r = (a_2)/(a_1) = (18)/(54) = (1)/(3) \\r = (a_3)/(a_2) = (6)/(18) = (1)/(3)`

The general formula is:

`G_n = A_1 (r)^(n-1)`

Putting the values of a1 and r

`G_n = 54 . ((1)/(3))^(n-1)`

Hence,

The general formula for nth term of given sequence is:

`G_n = 54 . ((1)/(3))^(n-1)`