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Answer:
To find the first term \( a_1 \) of an arithmetic sequence where the 22nd term \( a_{22} \) is \(-44\) and the common difference \( d \) is \( 2 \), we can use the formula for the \( n \)-th term of an arithmetic sequence:
\[
a_n = a_1 + (n - 1) \cdot d
\]
Here, \( a_{22} = -44 \), \( n = 22 \), and \( d = 2 \). Plug these values into the formula:
\[
a_{22} = a_1 + (22 - 1) \cdot d
\]
\[
-44 = a_1 + 21 \cdot 2
\]
\[
-44 = a_1 + 42
\]
To find \( a_1 \), solve for \( a_1 \):
\[
a_1 = -44 - 42
\]
\[
a_1 = -86
\]
So, the first term \( a_1 \) of the arithmetic sequence is \(-86\).
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