Question

Write the recursive formula for the geometric sequence 3,12,48

Answer 1

`a_(n)` = 4
`a_(n-1)`

Explanation:

A recursive formula allows a term in the sequence to be found by multiplying the preceding term by the common ratio r

for a geometric sequence the common ratio r is

r =
`(a_(2) )/(a_(1) )`

where a₂ is the second term and a₁ is the first term

here a₁ = 3 and a₂ = 12 , then

r =
`(12)/(3)` = 4

the recursive formula is then

`a_(n)` = 4
`a_(n-1)`