4. Given the explicit formula, find the 5th term.

Question

an = −5 + 10(n − 1)
A) 35
B) 10
C) -25
D) 45

6. Which function gives the correct recursive formula for the sequence? 2, 7, 12, 17, 22, 27
A) a1 = 5; an = an −1 + 2
B) a1 = 7; an = an −1 + 2
C) a1 = 2; an = an −1 + 7
D) a1 = 2; an = an −1 + 5

7. A car has 121,358 miles on its odometer and accumulates an average of 255 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks?
A) M(w) = 121,358w + 255w
B) M(w) = 121,358 + 255w
C) M(w) = 121,358w + 255
D) M(w) = 121,358 + 255

Answer 1

Let's analyze and solve each question one by one.

4. To find the 5th term of the sequence defined by the formula \( a_n = -5 + 10(n - 1) \), we plug in \( n = 5 \).

\[ a_5 = -5 + 10(5 - 1) = -5 + 10(4) = -5 + 40 = 35 \]

So, the answer is A) 35.

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6. The sequence given is: 2, 7, 12, 17, 22, 27.

To create a recursive formula, we need to identify the first term and the relationship between consecutive terms.

The first term \( a_1 = 2 \). The difference between consecutive terms is 5 (7 - 2 = 5, 12 - 7 = 5, etc.). Thus, the recursive formula should involve adding 5 to the previous term.

So the correct choice is D) a1 = 2; an = an − 1 + 5.

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7. To create a function that represents the total number of miles \( M \) the car will have on the odometer after \( w \) weeks:

The car starts with 121,358 miles and accumulates 255 more miles each week. So, after \( w \) weeks, the total mileage can be expressed as:

\[ M(w) = 121,358 + 255w. \]

Thus, the correct function is B) M(w) = 121,358 + 255w.