Write the first five terms of the geometric sequence if the nth term is given by 36 (1/3) ^n-1

G1=36, G2=12, G3=4, G4=4/3, G5=4/9

Step-by-step explanation:

Since the nth term is given by;

Gn = 36 (1/3) ^n-1, then, substitute the values of n as 1,2,3,4 and 5 to get the values of G1, G2, G3, G4 and G5 respectively.

G1=36 (1/3) ^1-1 = 36

G2 = 36 (1/3) ^2-1 = 12

G3 = 36 (1/3) ^3-1 = 4

G4 = 36 (1/3) ^4-1 = 4/3

G5 = 36 (1/3) ^5-1=4/9

36, 12, 4, 4/3, 4/9.

Step-by-step explanation:

We find each term by substituting the sequence number.

So the first term (where n = 1)

= 36 (1/3) ^ (1-1)

= 36 (1/3) ^0

= 36 * 1

= 36.

The second term is 36 (1/3) ^ (2-1) = 36 * 1/3

= 12.

We can find subsequent terms by just multiplying the previous term by 1/3 so the third term = 12 * 1/3 = 4.

So the first 5 terms are 36, 12, 4, 4/3, 4/9.