Question

Find the next term of the following sequence.9, 6, 4, ...A) 2B) 8/3C) 3

Answer 1

8/3. Option B is correct

Explanations:

The given sequence 9, 6, 4... is a geometric sequence. The nth term of the geometric sequence is expressed as:

`T_n=ar^(n-1)`

where:

a is the first term

n is the number of terms

r is the common ratio

From the sequence;

a = 9

r = 6/9 = 4/6 = 2/3

n = 4 (we need the 4th term)

Substitute the given parameters into the formula

`\begin{gathered} T_4=9((2)/(3))^(4-1) \\ T_4=9((2)/(3))^3 \\ T_4=\cancel{9}(\frac{8}{\cancel{27}^3}) \\ T_4=(8)/(3) \end{gathered}`

Hence the next term of the sequence is 8/3