Question

Find the first four terms of the recursive sequence defined by the following formula:

Answer 1

Answer:

144, 36, 9, 21/4

Step-by-step explanation:

Answer 2

Answer:

144, 36, 9, 2 $\frac{1}{4}$

Step-by-step explanation:

The recursive formula allows us to find a term in a sequence from the previous term.

Given

$a_{n}$ = $\frac{a_{n-1} }{4}$

Given the fourth term we require to work back to the third term , second and so on. Rearrange the formula to give

Multiply both sides by 4, then

$a_{n-1}$ = 4$a_{n}$

Given a₄ = 2 $\frac{1}{4}$, then

a₃ = 4 × a₄ = 4 × 2$\frac{1}{4}$ = 9

a₂ = 4 × a₃ = 4 × 9 = 36

a₁ = 4 × a₂ = 4 × 36 = 144