Question

Write a recursive rule for the sequence. X, X, 2x, 3x, 5x, 8x, ...

Answer 1

Answer:

The recursive rule for the sequence is

$a_{1}$ = x

$a_{2}$ = x

$a_{n}$ = $a_{n-1}$ + $a_{n-2}$

Step-by-step explanation:

∵ The first term is x

∴ $a_{1}$ = x

∵ The second term is x

∴ $a_{2}$ = x

∵ The third term is 2x

- That means the third term is the sum of the 1st and 2nd terms

∴ $a_{3}$ = $a_{1}$ + $a_{2}$

∵ The fourth term is 3x

∴ $a_{4}$ = $a_{2}$ + $a_{3}$

∵ The fifth term is 5x

∴ $a_{5}$ = $a_{3}$ + $a_{4}$

∵ The sixth term is 8x

∴ $a_{6}$ = $a_{4}$ + $a_{5}$

From all above the sequence is Fibonacci sequence where its recursive rule is

$a_{1}$ = first term

$a_{2}$ = second term

$a_{n}$ = $a_{n-1}$ + $a_{n-2}$

The recursive rule for the sequence is

$a_{1}$ = x

$a_{2}$ = x

$a_{n}$ = $a_{n-1}$ + $a_{n-2}$