## Jimboslice one year ago The following function defines a recursive sequence. f(0) = -5 f(1) = 20 f(n) = -4•f(n -1) - 3•f(n - 2); for n > 1 Which of the following sequences is defined by this recursive function? -5, -20, -65, -200, … -5, 20, -92, 372, … -5, -24, -92, -372, … -5, 20, -65, 200, …

1. amistre64

what is the first term?

2. Jimboslice

f(0) = -5 ?

3. amistre64

yes, so they give you the first one what is the second term?

4. amistre64

we can narrow the options by eliminating the ones that have the wrong first and second terms, then the third term gets us to only one option that fits

5. amistre64

we can use the rule given to determine f(2) f(n) = -4•f(n -1) - 3•f(n - 2) f(2) = -4•f(2 -1) - 3•f(2 - 2) f(2) = -4•f(1) - 3•f(0) ^^ ^^ we already know these values to plug into the rule

6. Jimboslice

ok so what now ?

7. amistre64

that IS the "what now" you work it out

8. amistre64

9. Jimboslice

oh ok hold on

10. Jimboslice

i dont get what im suppose to work out ....

11. amistre64

f(n) = -4•f(n -1) - 3•f(n - 2) f(2) = -4•f(2 -1) - 3•f(2 - 2) f(2) = -4•f(1) - 3•f(0) ^^ ^^ we already know these values to plug into the rule

12. amistre64

f(0) = -5 f(1) = 20

13. amistre64

wherever you see f(0), replace it by -5 wherever you see f(1), replace it by 20

14. Jimboslice

what if i see f(2)

15. amistre64

f(2) is what we are calculating ... f(2) will equal ______________

16. Jimboslice

f(2) = -4•f(1) - 3•f(0) =-65 correct?

17. amistre64

very good :)

18. amistre64

so what we are looking for is a sequence that starts out: f(0), f(1), f(2) -5, 20, -65 only one of the options starts out like this

19. Jimboslice

the last one ..

20. amistre64

correct

21. Jimboslice

thank you very much for explaining

22. amistre64

good luck :)