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14. Find 
f(2).

Write the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.
a. 
quad a(1)=7,a(n)=3a(n-1)-2 for 
n >= 2
b. 
quad b(1)=2,b(n)=2*b(n-1) for 
n >= 2.
c. 
c(1)=3,c(n)=c(n-1)-4 for 
n >= 2.
d. 
d(1)=3,d(n)=n*d(n-1) for 
n >= 2.

Type a response
REQUIRED
15. Find 
f(1).
a. 
2,4,6,8,10
b. 
(1)/(4),2,16,128,1024
11
c. 
120,60,0,-60,-120
(From Unit 1, Lesson 1.)
12
Type a response
3. Function 
f is defined by 
f(x)=3x-4 and 
g is defined by 
g(x)=4^(x).
a. Find 
f(3),f(2),f(1),f(0), and 
f(-1).
b. Find 
g(3),g(2),g(1),g(0), and 
g(-1).
(From Unit 1, Lesson 3.)
(13)(14) 16 (17)
(18) (19) 2122
REQUIRED
1
16. Find 
f(0).
Type a response

zoom in\newline14.14. Find f(2)f(2).\newlineWrite the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.\newlinea. \quad a(11)=77,\ a(n)=33a(n1-1)2-2 for n \geq 22\newlineb. \quad b(11)=22,\ b(n)=22\cdot b(n1-1) for n \geq 22.\newlinec. \quad c(11)=33,\ c(n)=c(n1-1)4-4 for n \geq 22.\newlined. \quad d(11)=33,\ d(n)=n\cdot d(n1-1) for n \geq 22.\newlineType a response\newlineREQUIRED\newline15.15. Find f(1)f(1).\newlinea. \quad 22,44,66,88,1010\newlineb. \quad \frac{11}{44},22,1616,128128,10241024\newline1111\newlinec. \quad 120120,6060,00,60-60,120-120\newline(From Unit 11, Lesson 11.)\newline1212\newlineType a response\newline33. Function ff is defined by f(x)=3x4f(x)=3x-4 and gg is defined by g(x)=4xg(x)=4^{x}.\newlinea. Find f(3),f(2),f(1),f(0),f(3),f(2),f(1),f(0), and f(1)f(-1).\newlineb. Find g(3),g(2),g(1),g(0),g(3),g(2),g(1),g(0), and g(1)g(-1).\newline(From Unit 11, Lesson 33.)\newline(1313)(1414) 1616 (1717)\newline(1818) (1919) 21222122\newlineREQUIRED\newline11\newline16.16. Find f(0)f(0).\newlineType a response

Full solution

Q. zoom in\newline14.14. Find f(2)f(2).\newlineWrite the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.\newlinea. \quad a(11)=77,\ a(n)=33a(n1-1)2-2 for n \geq 22\newlineb. \quad b(11)=22,\ b(n)=22\cdot b(n1-1) for n \geq 22.\newlinec. \quad c(11)=33,\ c(n)=c(n1-1)4-4 for n \geq 22.\newlined. \quad d(11)=33,\ d(n)=n\cdot d(n1-1) for n \geq 22.\newlineType a response\newlineREQUIRED\newline15.15. Find f(1)f(1).\newlinea. \quad 22,44,66,88,1010\newlineb. \quad \frac{11}{44},22,1616,128128,10241024\newline1111\newlinec. \quad 120120,6060,00,60-60,120-120\newline(From Unit 11, Lesson 11.)\newline1212\newlineType a response\newline33. Function ff is defined by f(x)=3x4f(x)=3x-4 and gg is defined by g(x)=4xg(x)=4^{x}.\newlinea. Find f(3),f(2),f(1),f(0),f(3),f(2),f(1),f(0), and f(1)f(-1).\newlineb. Find g(3),g(2),g(1),g(0),g(3),g(2),g(1),g(0), and g(1)g(-1).\newline(From Unit 11, Lesson 33.)\newline(1313)(1414) 1616 (1717)\newline(1818) (1919) 21222122\newlineREQUIRED\newline11\newline16.16. Find f(0)f(0).\newlineType a response
  1. Calculate first five terms: For sequence a, given a(1)=7 a(1) = 7 and a(n)=3a(n1)2 a(n) = 3a(n-1) - 2 for n2 n \geq 2 .\newlineCalculate the first five terms.\newlinea(1)=7 a(1) = 7 \newlinea(2)=3a(1)2=3(7)2=212=19 a(2) = 3a(1) - 2 = 3(7) - 2 = 21 - 2 = 19 \newlinea(3)=3a(2)2=3(19)2=572=55 a(3) = 3a(2) - 2 = 3(19) - 2 = 57 - 2 = 55 \newlinea(4)=3a(3)2=3(55)2=1652=163 a(4) = 3a(3) - 2 = 3(55) - 2 = 165 - 2 = 163 \newlinea(5)=3a(4)2=3(163)2=4892=487 a(5) = 3a(4) - 2 = 3(163) - 2 = 489 - 2 = 487
  2. Determine sequence type: Determine if sequence a is arithmetic, geometric, or neither.\newlineCheck the differences: 197=12 19 - 7 = 12 , 5519=36 55 - 19 = 36 , 16355=108 163 - 55 = 108 , 487163=324 487 - 163 = 324 \newlineThe differences are not constant, so it's not arithmetic.\newlineCheck the ratios: 19/72.71 19/7 \approx 2.71 , 55/192.89 55/19 \approx 2.89 , 163/552.96 163/55 \approx 2.96 , 487/1632.99 487/163 \approx 2.99 \newlineThe ratios are not constant, so it's not geometric.\newlineConclusion: Neither.
  3. Calculate first five terms: For sequence b, given b(1)=2 b(1) = 2 and b(n)=2b(n1) b(n) = 2b(n-1) for n2 n \geq 2 .\newlineCalculate the first five terms.\newlineb(1)=2 b(1) = 2 \newlineb(2)=2b(1)=2(2)=4 b(2) = 2b(1) = 2(2) = 4 \newlineb(3)=2b(2)=2(4)=8 b(3) = 2b(2) = 2(4) = 8 \newlineb(4)=2b(3)=2(8)=16 b(4) = 2b(3) = 2(8) = 16 \newlineb(5)=2b(4)=2(16)=32 b(5) = 2b(4) = 2(16) = 32
  4. Determine sequence type: Determine if sequence b is arithmetic, geometric, or neither.\newlineCheck the differences: 42=2 4 - 2 = 2 , 84=4 8 - 4 = 4 , 168=8 16 - 8 = 8 , 3216=16 32 - 16 = 16 \newlineThe differences are not constant, so it's not arithmetic.\newlineCheck the ratios: 4/2=2 4/2 = 2 , 8/4=2 8/4 = 2 , 16/8=2 16/8 = 2 , 32/16=2 32/16 = 2 \newlineThe ratios are constant, so it's geometric.\newlineConclusion: Geometric.
  5. Calculate first five terms: For sequence c, given c(1)=3 c(1) = 3 and c(n)=c(n1)4 c(n) = c(n-1) - 4 for n2 n \geq 2 .\newlineCalculate the first five terms.\newlinec(1)=3 c(1) = 3 \newlinec(2)=c(1)4=34=1 c(2) = c(1) - 4 = 3 - 4 = -1 \newlinec(3)=c(2)4=14=5 c(3) = c(2) - 4 = -1 - 4 = -5 \newlinec(4)=c(3)4=54=9 c(4) = c(3) - 4 = -5 - 4 = -9 \newlinec(5)=c(4)4=94=13 c(5) = c(4) - 4 = -9 - 4 = -13
  6. Determine sequence type: Determine if sequence c is arithmetic, geometric, or neither.\newlineCheck the differences: 13=4 -1 - 3 = -4 , 5(1)=4 -5 - (-1) = -4 , 9(5)=4 -9 - (-5) = -4 , 13(9)=4 -13 - (-9) = -4 \newlineThe differences are constant, so it's arithmetic.\newlineConclusion: Arithmetic.
  7. Calculate first five terms: For sequence d, given d(1)=3 d(1) = 3 and d(n)=nd(n1) d(n) = n \cdot d(n-1) for n2 n \geq 2 .\newlineCalculate the first five terms.\newlined(1)=3 d(1) = 3 \newlined(2)=2d(1)=23=6 d(2) = 2 \cdot d(1) = 2 \cdot 3 = 6 \newlined(3)=3d(2)=36=18 d(3) = 3 \cdot d(2) = 3 \cdot 6 = 18 \newlined(4)=4d(3)=418=72 d(4) = 4 \cdot d(3) = 4 \cdot 18 = 72 \newlined(5)=5d(4)=572=360 d(5) = 5 \cdot d(4) = 5 \cdot 72 = 360
  8. Determine sequence type: Determine if sequence d is arithmetic, geometric, or neither.\newlineCheck the differences: 63=3 6 - 3 = 3 , 186=12 18 - 6 = 12 , 7218=54 72 - 18 = 54 , 36072=288 360 - 72 = 288 \newlineThe differences are not constant, so it's not arithmetic.\newlineCheck the ratios: 6/3=2 6/3 = 2 , 18/6=3 18/6 = 3 , 72/18=4 72/18 = 4 , 360/72=5 360/72 = 5 \newlineThe ratios are not constant, so it's not geometric.\newlineConclusion: Neither.

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