Chart A:

Question

week Paid amount
1 200
2 250
3 300
4 350
5 400
6 450

Chart B:
Week paid amount
1 200
2 220
3 240
4 260
5 280
6 300

Equation for both charts: A: y = 200 + 50(x-1) = 150+50x
B: y = 200 * 1.10^(x-1)

2. Suppose you are a new employee. You notice that each payment option describes a sequence and decide to use rules to help determine which option to take.
(a) Determine the iterative rule for each sequence. Show your work.
(b) Your friend trusts your tables in Problem 1, but wonders if you wrote the iterative rules correctly. Show two calculations to convince your friend that both your rules work.

My Answer: A)
m=(y2-y1)/(x2-x1)
(x1,y1)=(1,200)
(x2,y2)=(2,250)
m=(250-200)/(2-1)
=50/1
=50
y=50x+b
200=50(1)+b
200=50+b
b=200-50
=150
y=50x+150

B)
y=50x+150
x= week 3
y=50(3)+150
=150+150
=300

Did I do this correctly?

Answer 1

the first one is an arithmetic sequence
Tn = a + r(n-1) = 200 + 50 (n-1)
same with the second but a = 200 again but r = 20
Your way works just as well for the first one but I notice they used the word "sequence" and I do not understand what you did or the second one.

Answer 2

Your equation for part A is correct,
but your equation for part B is an exponential function, while the
sequence is linear, that is, it also forms an arithmetic sequence.
e.g. if x = 6, you would get 200*1.1^5 = 322.10 , not the 600 we need

the 2nd equation would be:
y = 200 + 20(x-1) = 180 + 20x