Question

The first five terms of a pattern are shown.

Answer 1

Answer:

C

Step-by-step explanation:

There is a common ratio between consecutive term in the sequence, that is

$\frac{3}{10}$ ÷ $\frac{3}{100}$ = 3 ÷ $\frac{3}{10}$ = 30 ÷ 3 = 300 ÷ 30 = 10

This indicates the sequence is geometric with n th term

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r the common ratio

Here a = $\frac{3}{100}$ and r = 10 , thus

$a_{n}$ = $\frac{3}{100}$ $(10)^{n-1}$

    = $\frac{3}{10^{2} }$ × $10^{n-1}$

    = 3 × $10^{-2}$ × $10^{n-1}$

    = 3 × $10^{n-3}$

Thus

$a_{n}$ = 3$(10)^{n-3}$ → C