zoom in14. 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 \geq 2b. \quad b(1)=2,\ b(n)=2\cdot b(n−1) for n \geq 2.c. \quad c(1)=3,\ c(n)=c(n−1)−4 for n \geq 2.d. \quad d(1)=3,\ d(n)=n\cdot d(n−1) for n \geq 2.Type a responseREQUIRED15. Find f(1).a. \quad 2,4,6,8,10b. \quad \frac{1}{4},2,16,128,102411c. \quad 120,60,0,−60,−120(From Unit 1, Lesson 1.)12Type a response3. Function f is defined by f(x)=3x−4 and g is defined by g(x)=4x.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) 2122REQUIRED116. Find f(0).Type a response
Q. zoom in14. 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 \geq 2b. \quad b(1)=2,\ b(n)=2\cdot b(n−1) for n \geq 2.c. \quad c(1)=3,\ c(n)=c(n−1)−4 for n \geq 2.d. \quad d(1)=3,\ d(n)=n\cdot d(n−1) for n \geq 2.Type a responseREQUIRED15. Find f(1).a. \quad 2,4,6,8,10b. \quad \frac{1}{4},2,16,128,102411c. \quad 120,60,0,−60,−120(From Unit 1, Lesson 1.)12Type a response3. Function f is defined by f(x)=3x−4 and g is defined by g(x)=4x.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) 2122REQUIRED116. Find f(0).Type a response
Calculate first five terms: For sequence a, given a(1)=7 and a(n)=3a(n−1)−2 for n≥2.Calculate the first five terms.a(1)=7a(2)=3a(1)−2=3(7)−2=21−2=19a(3)=3a(2)−2=3(19)−2=57−2=55a(4)=3a(3)−2=3(55)−2=165−2=163a(5)=3a(4)−2=3(163)−2=489−2=487
Determine sequence type: Determine if sequence a is arithmetic, geometric, or neither.Check the differences: 19−7=12, 55−19=36, 163−55=108, 487−163=324The differences are not constant, so it's not arithmetic.Check the ratios: 19/7≈2.71, 55/19≈2.89, 163/55≈2.96, 487/163≈2.99The ratios are not constant, so it's not geometric.Conclusion: Neither.
Calculate first five terms: For sequence b, given b(1)=2 and b(n)=2b(n−1) for n≥2.Calculate the first five terms.b(1)=2b(2)=2b(1)=2(2)=4b(3)=2b(2)=2(4)=8b(4)=2b(3)=2(8)=16b(5)=2b(4)=2(16)=32
Determine sequence type: Determine if sequence b is arithmetic, geometric, or neither.Check the differences: 4−2=2, 8−4=4, 16−8=8, 32−16=16The differences are not constant, so it's not arithmetic.Check the ratios: 4/2=2, 8/4=2, 16/8=2, 32/16=2The ratios are constant, so it's geometric.Conclusion: Geometric.
Calculate first five terms: For sequence c, given c(1)=3 and c(n)=c(n−1)−4 for n≥2.Calculate the first five terms.c(1)=3c(2)=c(1)−4=3−4=−1c(3)=c(2)−4=−1−4=−5c(4)=c(3)−4=−5−4=−9c(5)=c(4)−4=−9−4=−13
Determine sequence type: Determine if sequence c is arithmetic, geometric, or neither.Check the differences: −1−3=−4, −5−(−1)=−4, −9−(−5)=−4, −13−(−9)=−4The differences are constant, so it's arithmetic.Conclusion: Arithmetic.
Calculate first five terms: For sequence d, given d(1)=3 and d(n)=n⋅d(n−1) for n≥2.Calculate the first five terms.d(1)=3d(2)=2⋅d(1)=2⋅3=6d(3)=3⋅d(2)=3⋅6=18d(4)=4⋅d(3)=4⋅18=72d(5)=5⋅d(4)=5⋅72=360
Determine sequence type: Determine if sequence d is arithmetic, geometric, or neither.Check the differences: 6−3=3, 18−6=12, 72−18=54, 360−72=288The differences are not constant, so it's not arithmetic.Check the ratios: 6/3=2, 18/6=3, 72/18=4, 360/72=5The ratios are not constant, so it's not geometric.Conclusion: Neither.
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