Question

consider the arithmetic sequence \\(27, 40, 53, 66, 79, \dots\\)

what rule can be used to find the next term of the sequence?

\\(a_n = a_{n-1} - 79\\)
\\(a_n = a_{n-1} - 13\\)
\\(a_n = a_{n-1} + 13\\)
\\(a_n = a_{n-1} + 79\\)

Explanation:

Identify the common difference

Using the Arithmetic Sequences knowledge point

$$ d = 40 - 27 = 13 $$

$$ 53 - 40 = 13 $$

$$ 66 - 53 = 13 $$

$$ 79 - 66 = 13 $$

Formulate the recursive rule

The next term \(a_n\) is found by adding the common difference \(d = 13\) to the previous term \(a_{n-1}\):

$$ a_n = a_{n-1} + 13 $$

Answer:

• (A) \(a_n = a_{n-1} - 79\)
• (B) \(a_n = a_{n-1} - 13\)
• (C) \(a_n = a_{n-1} + 13\) (Correct answer)
• (D) \(a_n = a_{n-1} + 79\)