Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence?

f(1) = 6, f(4) = 12, f(7) = 18

f (n + 1) = f(n) + 6
f (n + 1) = 2f(n)
f (n + 1) = f(n) + 2
f (n + 1) = 1.5f(n)

Question

Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence?

f(1) = 6, f(4) = 12, f(7) = 18

f (n + 1) = f(n) + 6
f (n + 1) = 2f(n)
f (n + 1) = f(n) + 2
f (n + 1) = 1.5f(n)

Vocaloid · Answer

it's arithmetic which automatically eliminates B and D as these are geometric sequences

to find d, plug in the first two terms into the formula

an = a1 + (n-1)d, since we are working w/ terms 1-4 we use n = 4 and solve for d

then the recursive formula should be clear from there