Question

given the recursive formula for the arithmetic sequence ( a_1 = 22 ), ( a_n = a_{n - 1} - 10 ), find the second term of the sequence. (1 point)
( \bigcirc ) ( a_2 = 12 )
( \bigcirc ) ( a_2 = 11 )
( \bigcirc ) ( a_2 = 2 )
( \bigcirc ) ( a_2 = -9 )

Explanation:

Step1: Identify the formula for \(a_2\)

For a recursive arithmetic sequence, to find \(a_2\), we use \(n = 2\) in the formula \(a_n=a_{n - 1}-10\). So \(a_2=a_{2 - 1}-10=a_1 - 10\).

Step2: Substitute \(a_1\) value

We know \(a_1 = 22\), so substitute into the formula: \(a_2=22 - 10\).

Step3: Calculate the result

\(22-10 = 12\), so \(a_2 = 12\).

Answer:

\(a_2 = 12\) (corresponding to the option: \(a_2 = 12\))