Write a recursive formula for the following sequences:

Question

1) 1,6,11,16...
2) 4, 12, 36, 108...

3) A ball is dropped from an initial height of 10 feet. The maximum heights the ball bounces are as shown (10 ft, 6 ft, 3.6 ft, 2.16 ft)
a-write a recursive formula
b-write an explicit formula

*basically, I don't know how to write a recursive or explicit formula*

Answer 1

#1
clearly you have to add 5 each time, so

T(n+1) = T(n) + 5
explicitly, that means

T(n) = -4 + 5n

You can do the others similarly.

Answer 2

Thank you!
One more question: how do you change an explcit formula to a recursive formula and vice versa?

Answer 3

it's not always easy.

Thus, since you know that #1 adds 5 each time, you expect

T(n) = 5n
But, T(1) = 5*1=5, not 1, so adjust the starting term:

T(1) = 5*1-4
T(n) = 5n-4 or, -4+5n

Answer 4

Thanks!