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mars1129 [50]
3 years ago
13

Please help fast if appreciate it! For 2A and 2B. Show your work please so I can understand and I’ll mark brainlist!

Mathematics
1 answer:
Neporo4naja [7]3 years ago
5 0
2a. y - y1 = m(x - x1)
m = (7-3)/(5 + 1) = 4/6 = 2/3
y1 = 7, x1 = 5
y - 7 = 2/3(x - 5)

2b. Slope intercept form: y = mx + b
y = 2/3(x -5) + 7
y = 2/3x -10/3 + 7
y = 2/3x - 10/3 + 21/3
Y = 2/3x + 11/3
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These are the first six terms of a sequence with a1= -7:
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The recursive formula for this sequence is a_{1} = -7;  a_{n} = a_{n-1} + 10

Step-by-step explanation:

The recursive formula of the arithmetic sequence is:

a_{1} = first term;  a_{n} = a_{n-1} + d

  • a_{1} is the first term in the sequence  
  • a_{n} is the nth term in the sequence  
  • a_{n-1}  the term before the nth term  
  • n is the term number
  • d is the common difference

∵ The sequence is -7 , 3 , 13  , 23 , 33 , 43 , ........

∵ 3 - (-7) = 3 + 7 = 10

∵ 13 - 3 = 10

∵ 23 - 13 = 10

- There is a constant difference 10 between the consecutive terms

∴ The sequence is an arithmetic sequence

∵ The first term is -7

∴ a_{1} = 7

∵ The common difference is 10

∴ d = 10

- Substitute in the formula above a_{1} by -7 and d by 10

∴ a_{1} = -7;  a_{n} = a_{n-1} + 10

To check the formula find the second term

∵ n = 2

∴ a_{1} = -7;  n_{2} = n_{2-1} + 10

∴  n_{2} = n_{1} + 10

∵ n_{1}  = -7

∴ n_{2} = -7 + 10 = 3 which is right

The recursive formula for this sequence is a_{1} = -7;  a_{n} = a_{n-1} + 10

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

#LearnwithBrainly

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