Find the 57th term of the sequence:
Given sequence: [tex]\(13, 8, 3, -2, -7, -12, \ldots\)[/tex]
1. Enter the common difference:
[tex]\[ \text{common difference} = 8 - 13 \][/tex]
2. Use the formula for the [tex]\(n\)[/tex]-th term of an arithmetic sequence:
[tex]\[ a_n = a_1 + (n-1)d \][/tex]
3. Find the 57th term:
[tex]\[ a_{57} = 13 + (57-1)(-5) \][/tex]