SOLUTION: Find the first five terms of the recursive sequence defined by the function below. 𝑓(𝑛) = 2𝑓(𝑛 − 1) + 3𝑛, where 𝑓(1) = &#872

Algebra ->  Sequences-and-series -> SOLUTION: Find the first five terms of the recursive sequence defined by the function below. 𝑓(𝑛) = 2𝑓(𝑛 − 1) + 3𝑛, where 𝑓(1) = &#872      Log On


   



Question 1049962: Find the first five terms of the recursive
sequence defined by the function below.
𝑓(𝑛) = 2𝑓(𝑛 − 1) + 3𝑛, where 𝑓(1) = −2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the first five terms of the recursive sequence defined by the function below.
f%28n%29+=+2f%28n-+1%29+%2B+3n, where f%281%29+=+-2
if f%281%29+=+-2, means first term is
+a%5B1%5D=-2
then
n=2
-> 2f%282-1%29+%2B+3%2A2-> 2f%281%29+%2B+6-> 2%28-2%29+%2B+6->-4%2B6=2
a%5B2%5D=+2...second term
n=3
-> 2f%283-1%29+%2B+3%2A3-> 2f%282%29+%2B+9-> 2%282%29+%2B9->4%2B9=13
a%5B3%5D=+13...third term
n=4
-> 2f%284-1%29+%2B+3%2A4-> 2f%283%29+%2B+12-> 2%2813%29+%2B12->26%2B12=38
a%5B4%5D=+38.....forth term

n=5
-> 2f%285-1%29+%2B+3%2A5-> 2f%284%29+%2B+15->+2%2838%29+%2B15->76%2B15=91
a%5B5%5D=+91
so,the first five terms of the recursive sequence are:+-2,+2,+13,+38,+91,.....