Algebra 1 Common Core Student Edition, Grade 8-9

4 Lesso n Ch eck^

Do yo u k n o w H OW?

Are the following geometric sequences? If so, find the

common ratio.

1. 3, 9, 27,81,...


2. 200,50, 12.5,3.125,...


3. 10, 8, 6, 4,...
   Write the explicit and recursive formulas for each
   geometric sequence.


4. 5, 20, 80, 3 2 0 ,... 5. 4, - 8 , 16, - 3 2 ,...


5. 162, 108, 72, 4 8 ,... 7. 3, 6, 12, 2 4 ,...

__ MATHEMATICAL

Do yo u UN DERSTAND? U 9 f PRACTICES

8. E rro r A n alysis A friend says th a t the

recursive form ula for the geom etric sequence

1, - 1 , 1 , - 1 , 1 ,... i s an = 1 • (-1 )"-1. Explain your

friend's error a n d give the correct recursive form ula

for the sequence.

9. Critical Thinking D escribe th e sim ilarities and
   differences b etw een arithm etic an d geom etric
   sequences.

MATHEMATICAL

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses PRACTICES

Q Practice Determine whether the sequence is a geometric sequence. Explain

10. 2, 8, 32, 1 2 8 ,...


11. 256, 1 9 2 ,1 4 4 ,1 0 8 ,...
    11. 5, 10, 15, 2 0 ,...
    14. 6, - 1 2 , 2 4 , - 4 8 ,...

Find the common ratio for each geometric sequence.

16. 3, 6 ,12, 2 4 ,... 17. 81, 27, 9, 3 ,...


17. 5, 20, 80, 3 2 0 ,... 20. 7, - 7 , 7, - 7 ,...

Write the explicit formula for each geometric sequence.

22. 2,6,18, 5 4 ,... 23. 3, 6 ,1 2 , 2 4 ,...


23. 3, - 1 2 , 4 8 , - 1 9 2 ,... 26. 8, - 8 , 8, - 8 ,...

Write the recursive formula for each geometric sequence.

28. 4,8,16, 3 2 ,... 29. 1, 5 ,2 5 ,1 2 5 ,...
    31.2,-8,32,-64,... 32. J J 36’ 12’ 4’ 4’1 3

4R See Problem 1.

12. 162,54,18,6,...


13. 10,20,40,80,...


14. 128,96,72,54,...


15. 2,-6,18,-54,...

See Problem 2.

24. 200, 40, 8, l | ,...


25. 686, 98, 14, 2 ,...


26. 100, 50, 25, 1 2 .5 ,...


27. 192,128, 85|, 56§,. ..


28. Science W hen a radioactive su b stan ce decays, m easu rem en ts of th e a m o u n t ^9 See Problem 3.
    rem aining over co n stan t intervals of tim e form a geom etric sequence. I h e table
    shows th e a m o u n t of FI-18, rem aining after different
    co n stan t intervals. Write th e explicit a n d recursive
    form ulas for th e geom etric sequence form ed by the
    am o u n t of FI-18 rem aining.

Fluorine-18 Remaining

Time (min) (^0110220330)
FI-18 (picogram s) 260 130
65
32.5
470 Ch ap t er 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s