Algebra 1 Common Core Student Edition, Grade 8-9

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35. A store m anager plans to offer discounts on som e sweaters according to this sequence:
    $48, $36, $27, $ 2 0 .2 5 ,... Write the explicit an d recursive formulas for the sequence.


36. A geom etric sequence has an initial value of 18 a n d a co m m o n ratio of W rite a ^ See Problem 4.
    function to rep resen t this sequence. G raph th e function.


37. W rite an d graph th e function th a t represents
    the sequence in th e table. X^1234
    f(x) 81632 64

Determine if each sequence is a geometric sequence. If it is, find the common

ratio and write the explicit and recursive formulas.

38. 5,10, 2 0 ,4 0 ,...


39. 98,14,2 ,|,...
    39. 20,15,10,5,...


40. -3 ,-1 ,1 ,3 ,...

Identify each sequence as arithmetic, geometric, or neither.

44. 1.5, 4.5, 13.5, 4 0 .5 ,... 45. 42, 38, 34, 3 0 ,...
    47.-4,1,6,11,... 48.1,2,3,5,...
    40. 3, - 9 , 27, - 8 1 ,...
    43. 200,-100, 5 0 ,-2 5 ,...
    46. 4, 9 ,1 6 , 2 5 ,...
    49. 2, 8 , 3 2 , 1 2 8 ,...


45. Think about a Plan Suppose you are reh earsin g for a concert. You p la n to reh earse
    th e piece you will perform four tim es th e first day an d th e n to double th e n u m b e r of
    tim es you reh earse th e piece each day until th e concert. W hat are two form ulas you
    can write to describe th e seq u e n ce of how m any tim es you will reh earse the piece
    each day?

• How can you write a seq u e n ce of n u m b ers to re p resen t this situation?


• Is the seq u en ce arithm etic, geom etric, or neither?


• How can you write explicit a n d recursive form ulas for this sequence?

51. Open-Ended Write a geom etric sequence. Then w rite th e explicit an d recursive
    form ulas for your sequence.
    fjyyj^y 5 2. Science A certain culture of yeast increases by 50% every th ree hours. A scientist
    places 9 gram s of th e yeast in a culture dish. W rite th e explicit an d recursive
    form ulas for the geom etric seq u en ce form ed by th e grow th of th e yeast.
    Challenge 53. The differences b etw een consecutive term s in a geom etric seq u en ce form a
    new geom etric sequence. For instance, w h e n you take th e differences betw een
    the consecutive term s of th e geom etric seq u en ce 5 ,1 5 ,4 5 ,1 3 5 ,... you get
    15 — 5,45 — 15,135 — 4 5 ,... The n ew geom etric seq u e n ce is 10, 30, 9 0 ,...
    C om pare th e two sequences. How are they similar, an d how do they differ?

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PowerAlgebra.com I L e s s o n 7 - 8 Geometric Sequences

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