Question

Given the recursive formula for the arithmetic sequence a1=22
𝑎
1
=
22
, an=an−1−10
𝑎
𝑛
=
𝑎
𝑛
−
1
−
10
, find the second term of the sequence.(1 point)
Responses

a2=2
𝑎
2
=
2
a subscript 2 baseline equals 2

a2=−9
𝑎
2
=
−
9
a subscript 2 baseline equals negative 9

a2=12
𝑎
2
=
12
a subscript 2 baseline equals 12

a2=11

Answer 1

To find the second term of the arithmetic sequence given the recursive formula, we start with the initial term \( a_1 \) and use the formula to compute \( a_2 \).

Given:
- \( a_1 = 22 \)
- \( a_n = a_{n-1} - 10 \)

We can find \( a_2 \) using the recursive formula:

\[
a_2 = a_1 - 10
\]
\[
a_2 = 22 - 10
\]
\[
a_2 = 12
\]

Thus, the second term \( a_2 \) of the sequence is:

\[
\boxed{12}
\]