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\\)

the next two terms are \\(92\\) and \\(105\\).

the twentieth term of the sequence is \\(274\\). what is the twenty-first term of the sequence?

the twenty-first term is

Explanation:

Find the common difference

Using the Arithmetic Sequences knowledge point

$$ d = 40 - 27 = 13 $$

Apply the recursive formula

Using the Recursive Formulas knowledge point

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

Calculate the twenty-first term

Using the Arithmetic Sequences knowledge point

$$ a_{21} = a_{20} + d = 274 + 13 = 287 $$

Answer:

The twentieth term of the sequence is 274. What is the twenty-first term of the sequence?

The twenty-first term is <blank>287</blank>