Question

select the correct answer.

which type of sequence is shown?

(5, 10, 15, 20, 25, \dots)

• both arithmetic and geometric
• geometric
• arithmetic
• neither arithmetic nor geometric

Explanation:

⚡ Using what you learned: Recursive and Explicit Formulas

Step 1: Analyze differences between consecutive terms

Find the difference between each consecutive pair of terms in the sequence \( 5, 10, 15, 20, 25, \dots \):

$$ 10 - 5 = 5 $$

$$ 15 - 10 = 5 $$

$$ 20 - 15 = 5 $$

$$ 25 - 20 = 5 $$

Since there is a constant difference of \( 5 \) being added to get to the next term, the sequence is arithmetic.

Step 2: Analyze ratios between consecutive terms

Find the ratio between consecutive terms to check if it is geometric:

$$ \frac{10}{5} = 2 $$

$$ \frac{15}{10} = 1.5 $$

Since the ratios are not equal, there is no constant multiplier, so the sequence is not geometric.

Answer:

arithmetic