Question

write a recursive formula for the sequence 7, 4, 1, -2, -5, ...then find the next term.

Answer 1

@Hero

Answer 2

Hang on for a minute while I solve this

Answer 3

Okay, I have it

Answer 4

So the first thing you should do is create a chart of values (n , r)
(1, 7), (2, 4), (3, 1), (4, -2), (5, -5)

Answer 5

Then notice that

7 = 4 + 3
4 = 1 + 3
1 = -2 + 3
-2 = -5 + 3

And now notice this pattern

\(r_n = r_{(n + 1)} + 3\)

Answer 6

Can you see how to find the next term from here?