To solve for the 31st term in the arithmetic sequence given by [tex]\( a_n = 11 - 2(n - 1) \)[/tex]:
1. Identify the general form of the sequence: We are given that the arithmetic sequence is described by the formula [tex]\( a_n = 11 - 2(n - 1) \)[/tex].
2. Plug in [tex]\( n = 31 \)[/tex] into the formula to find [tex]\( a_{31} \)[/tex]:
[tex]\[
a_{31} = 11 - 2(31 - 1)
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
31 - 1 = 30
\][/tex]
4. Multiply by -2:
[tex]\[
-2 \times 30 = -60
\][/tex]
5. Add the result to 11:
[tex]\[
11 + (-60) = 11 - 60 = -49
\][/tex]
Therefore, the 31st term of the sequence, [tex]\( a_{31} \)[/tex], is [tex]\( -49 \)[/tex].
Thus, the correct solution is:
- [tex]\( a_n = 11 - 2(n - 1) ; a_{31} = -49 \)[/tex]
