Question

select the correct answer.

consider the arithmetic sequence.

-9, -2, 5, 12, ...

given that the sequence is represented by the function \\(f(n)\\), what are the values of \\(f(1)\\) and the common difference?

\\(f(1) = -9\\)
common difference: -7

\\(f(1) = -2\\)
common difference: -7

\\(f(1) = -2\\)
common difference: 7

\\(f(1) = -9\\)
common difference: 7

Explanation:

⚡ Using what you learned: Arithmetic Sequences

Step 1: Find the first term

The sequence is given as:

$$ -9, -2, 5, 12, \dots $$

The first term of the sequence, represented by \( f(1) \), is:

$$ f(1) = -9 $$

Step 2: Find the common difference

The common difference \( d \) is the difference between any consecutive terms:

$$ d = -2 - (-9) = 7 $$

$$ d = 5 - (-2) = 7 $$

$$ d = 12 - 5 = 7 $$

Thus, the common difference is \( 7 \).

Answer:

• \( f(1) = -9 \)
• Common difference: \( 7 \)

(This corresponds to the fourth option)