Question

Write the first five terms of the geometric sequence in which a1 = 27 and the common ratio is 4/3

a) 27,18, 12, 8, 16/3
b) 27, 9, 3, 1, 1/3
c) 27, 36, 48, 64, 256/3
d) 27, 9, 1/3, 4/9, 16/27

please explain

Answer 1

c) 27, 36, 48, 64, 256/3

Explanation:

We are given a geometric sequence with;

• First term, a = 27
• Common ratio, r = 4/3

We are supposed to write the sequence;

We know that a given term in a GP is given by;

`T_n=ar^n^-^1`, where a is the first term, n is the nth term

Therefore;

`First term, a = 27 \\Second term = ar^1= 27(4/3) = 36\\Third term = ar^2=27(4/3)^2=48\\Fourth term =ar^3=27(4/3)^3=64\\Fifth term = ar^4 = 27(4/3)^4 =(256)/(3) \\And so forth`

Therefore;

The geometric sequence is;

`27,36,48,64,(256)/(3)`