Question

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

$$\begin{cases} f(1) = 3 \\\\ f(n) = f(n-1) + 4 \\text{ if } n > 1 \\end{cases}$$

\\)

a) 3, 7, 11, 15
b) 3, 8, 10, 12
c) 3, 9, 11, 13
d) 4, 7, 10, 13

question 17 (5 points)
which of the following is an arithmetic sequence with common difference -5?

a) 5, -25, 125, -625, ...
b) 8, 3, -2, -7, ...
c) 0, 5, 10, 15, ...
d) 5, 25, 125, 625, ...

question 18 (5 points)
write an exponential equation for the geometric sequence 1, 10, 100, 1000, ...

a) \\( a_n = 10(1)^{n-1} \\)
b) \\( a_n = 10(0.1)^{n-1} \\)
c) \\( a_n = 1(10)^{n-1} \\)
d) \\( a_n = 10(10)^{n-1} \\)

Explanation:

Calculate the terms of the recursive sequence

$$
LATEXBLOCK0
$$

Identify the arithmetic sequence with common difference -5

$$
LATEXBLOCK1
$$

Determine the geometric sequence equation

$$
LATEXBLOCK2
$$

Answer:

Question 1

• A) 3, 7, 11, 15 (Correct answer)
• B) 3, 8, 10, 12
• C) 3, 9, 11, 13
• D) 4, 7, 10, 13

Question 17

• A) 5, -25, 125, -625, ...
• B) 8, 3, -2, -7, ... (Correct answer)
• C) 0, 5, 10, 15, ...
• D) 5, 25, 125, 625, ...

Question 18

• A) \(a_n = 10(1)^{n-1}\)
• B) \(a_n = 10(0.1)^{n-1}\)
• C) \(a_n = 1(10)^{n-1}\) (Correct answer)
• D) \(a_n = 10(10)^{n-1}\)