Question

a₁ = 2

aₙ = 9aₙ₋₁

write your answers as integers or fractions in simplest form.

a₂ =

a₃ =

Explanation:

Step1: Find \(a_2\)

To find \(a_2\), we use the recursive formula \(a_n = 9a_{n - 1}\) with \(n = 2\). This means we need to substitute \(n - 1 = 1\) into the formula, so we use \(a_1\) which is given as 2.
\(a_2 = 9a_{2 - 1}=9a_1\)
Substitute \(a_1 = 2\) into the equation:
\(a_2 = 9\times2 = 18\)

Step2: Find \(a_3\)

To find \(a_3\), we use the recursive formula \(a_n = 9a_{n - 1}\) with \(n = 3\). This means we need to substitute \(n - 1 = 2\) into the formula, so we use \(a_2\) which we just found to be 18.
\(a_3 = 9a_{3 - 1}=9a_2\)
Substitute \(a_2 = 18\) into the equation:
\(a_3 = 9\times18 = 162\)

Answer:

\(a_2 = 18\)
\(a_3 = 162\)