Question

The cost, in dollars, of making smoothies, for n ≥ 1, is represented by the sequence shown.

12, 15, 18, 21, 24, 27, ...
Complete the recursive formula for this sequence for n 1, and determine the initial value when n = 1.
f(n+1)=
f(1) =

Answer 1

Explanation:

it is not clear what n are represented by the given sequence.

is f(1) = n1 = 12 ?

is there any other basic cost involved that we have to start with ? if is it truly starting at $0, and every smoothie adds $3, as the sequence suggests ?

in other words, since we have no other information, we have to assume we really start at 0.

anyway,

f(n + 1) = f(n) + 3

f(0) = 0

f(1) = f(0) + 3 = $3

f(2) = f(1) + 3 = f(0) + 3 + 3 = $6

so, we see,

f(n + 1) = f(0) + 3(n + 1) = 0 + 3(n + 1) = 3(n + 1)

or simply

f(n) = 3n

if f(1) = 12 (the first number in the list),

then we have

f(n + 1) = f(n) + 3 = f(1) + 3n = 12 + 3n = 3(4 + n)