To find the 20th term of the given arithmetic sequence, we can follow these steps:
The general formula for the arithmetic sequence is given by:
[tex]\[ a(n) = -5 + (n-1) \cdot 3 \][/tex]
We want to find the 20th term, so we need to substitute [tex]\( n = 20 \)[/tex] into the formula.
Step 1: Substitute [tex]\( n = 20 \)[/tex] into the formula.
[tex]\[ a(20) = -5 + (20-1) \cdot 3 \][/tex]
Step 2: Simplify the expression inside the parentheses.
[tex]\[ a(20) = -5 + 19 \cdot 3 \][/tex]
Step 3: Multiply 19 by 3.
[tex]\[ a(20) = -5 + 57 \][/tex]
Step 4: Add -5 and 57.
[tex]\[ a(20) = 52 \][/tex]
Hence, the 20th term of the arithmetic sequence is:
[tex]\[ \boxed{52} \][/tex]
