Question

What is the answer for this?​

Answer 1

Answer:

The general formula for nth term of given sequence is:

$G_n = 54 . (\frac{1}{3})^{n-1}$

Step-by-step 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.

$Here\\a_1 = 54\\a_2 = 18\\a_3 = 6\\And\\r = \frac{a_2}{a_1} = \frac{18}{54} = \frac{1}{3} \\r = \frac{a_3}{a_2} = \frac{6}{18} = \frac{1}{3}$

The general formula is:

$G_n = A_1 (r)^{n-1}$

Putting the values of a1 and r

$G_n = 54 . (\frac{1}{3})^{n-1}$

Hence,

The general formula for nth term of given sequence is:

$G_n = 54 . (\frac{1}{3})^{n-1}$