Question

identify the common difference of the sequence: \\(-8, -1, 6, 13, \dots\\)

a) \\(-7\\)
b) \\(7\\)
c) \\(-6\\)
d) \\(6\\)

question 2 (5 points)
which of the following is an infinite series?

a) \\(3, -6, 12, -24, 48\\)
b) \\(4 + 8 + 16 + 32\\)
c) \\(2 - 6 + 18 - 54 + \dots\\)
d) \\(3, 13, 23, 33, \dots\\)

question 3 (5 points)
given the recursive formula shown, what are the first 4 terms of the sequence?
\\f(n) = \

$$\begin{cases} f(1) = 6 \\\\ f(n) = f(n-1) + 7 \\text{ if } n > 1 \\end{cases}$$

\\

a) \\(6, 42, 294, 2,058\\)
b) \\(6, 13, 20, 27\\)
c) \\(6, -1, -8, -15\\)
d) \\(7, 13, 19, 25\\)

Explanation:

Calculate the common difference of the sequence

$$ d = -1 - (-8) = 7 $$

$$ d = 6 - (-1) = 7 $$

$$ d = 13 - 6 = 7 $$

Identify the infinite series

An infinite series is the sum of infinitely many terms, indicated by addition/subtraction signs and ellipsis \(...\).

• Option A: Finite sequence (comma-separated, no ellipsis)
• Option B: Finite series (addition, no ellipsis)
• Option C: Infinite series (addition/subtraction, with ellipsis)
• Option D: Infinite sequence (comma-separated, with ellipsis)

Calculate the first 4 terms of the recursive sequence

$$
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$$

Answer:

Question 1

• (A) -7
• (B) 7 (Correct answer)
• (C) -6
• (D) 6

Question 2

• (A) 3, -6, 12, -24, 48
• (B) 4 + 8 + 16 + 32
• (C) 2 - 6 + 18 - 54 + ... (Correct answer)
• (D) 3, 13, 23, 33, ...

Question 3

• (A) 6, 42, 294, 2,058
• (B) 6, 13, 20, 27 (Correct answer)
• (C) 6, -1, -8, -15
• (D) 7, 13, 19, 25