Math Question Recursive Formula

Question

g(1)=4

g(n)=g(n-1)+3.2

g(3)= ________

Answer 1

Hi Kass,

The answer is below. g(n) represents a formula, which is defined for any value of n, with the starting point of g(1). To find g(3), you just need to walk your way along increasing values of n. Feel free to contact me if you need any further help!

For n=1

g(1)=4

For n=2

g(2) = g(2-1) + 3.2 = g(1) + 3.2 = 4 + 3.2 = 7.2

For n=3

g(3) = g(3-1) + 3.2 = g(2) + 3.2 = 7.2 + 3.2 = 10.4

What if you wanted to know g(100)? Would you have to chug through all those values of n? You certainly could, but you might notice along the way that all you're doing is adding 3.2 at each step! So instead of chugging, you can replace the recursive formula with a general formula, which describes a straight line, of slope 3.2, with y-intercept at 4. I'll leave it up to you to find that formula!