Write the first four terms of a geometric sequence. Using the values you have written, calculate the common ratio and write the rule for the nth term. Show all calculations.

FIRST FOUR (4) TERM = 6, 18, 54,162.

COMMON RATIO = 3

Step-by-step explanation:

In geometric expression.

Tn = the nth term

a = first term

r = common ratio.

Let's take the First term of the G.P as 6 and the third term as 54. Let's find the common ratio.

3rd term will be written as:

T3 = ar² = 54

Given the first term as 6.

T3 = 6r² = 54

6r² = 54

r² = 54 / 6

r² = 9

r= √9

r = 3

Therefore common ratio = 3.

Let's use this information to get the fourth term.

T4 = ar³

when a = 6

and r = 3.

T4 = 6 * 3³

T4 = 6 * 27

T4 = 162