Find an explicit formula for the geometric sequence -9,-12,-36,-72...

Question

You must provide your answer with the following format: c(n)

Answer 1

Greetings! Lets solve this shall we ?

So, we must find an explicit formula of this geometric sequence given -9, -12, -36, -72.... We yield the formula for geometric series to be

a_n = a₁(r)^n-1 ......... We find the common ratio to be the second term divided by the first term

a₂ / a₁ = r = (-12) / (-9) = 3. Finally we plug in a₁ = -9 and r = 3 to obtain our formula such that

a_n = -9(3)^n-1

I hope this helped!