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1. Using the equation t = 13n + 7, create a sequence that corresponds from the 1st term to the 5th term.

A) 20, 33, 46, 59, 72
B) 20, 33, 39, 59, 72
C) 13, 26, 39, 50, 65
D) 21, 22, 23, 24, 25

2. Create a formula for the points (1,5), (2,7), (3,9), and (4,11).
A) y = -2x - 3
B) y = 2x - 3
C) y = 2x + 3
D) y = -2x + 3

1 answer

  1. To generate a sequence using the equation \( t = 13n + 7 \), we can substitute \( n \) from 1 to 5:
  • For \( n = 1 \): \( t = 13(1) + 7 = 13 + 7 = 20 \)
  • For \( n = 2 \): \( t = 13(2) + 7 = 26 + 7 = 33 \)
  • For \( n = 3 \): \( t = 13(3) + 7 = 39 + 7 = 46 \)
  • For \( n = 4 \): \( t = 13(4) + 7 = 52 + 7 = 59 \)
  • For \( n = 5 \): \( t = 13(5) + 7 = 65 + 7 = 72 \)

The sequence is: 20, 33, 46, 59, 72

So the answer is A) 20, 33, 46, 59, 72.

  1. To create a formula for the points (1,5), (2,7), (3,9), and (4,11), we can look for a linear relationship.

Observing the values, we see that for every increase of 1 in \( x \) (1 to 2, 2 to 3, etc.), \( y \) increases by 2 (5 to 7, 7 to 9, etc.). This indicates a slope of 2.

Now, we can use the point-slope form to derive the equation. Choosing point (1, 5):

  1. The slope (m) is 2.
  2. Using the point-slope formula \( y - y_1 = m(x - x_1) \):

\[ y - 5 = 2(x - 1) \]

Distributing gives:

\[ y - 5 = 2x - 2 \]

Adding 5 to both sides results in:

\[ y = 2x + 3 \]

So the formula that fits these points is \( y = 2x + 3 \).

Thus, the answer is C) y = 2x + 3.