Answer:
The18th term of the given sequence is -128
Explanation:
To find the 18th term of the sequence:
42, 32, 22, 12, ..., we need to find the nth term of the sequence first.
The nth term of a sequence is given be the formula:
[tex]T_n=a+(n-1)d[/tex]Where a is the first term, and d is the common difference.
Here, a = 42, d = 32 - 42 = -10
[tex]\begin{gathered} T_n=42+(n-1)(-10) \\ =42-10n+10 \\ T_n=52-10n \end{gathered}[/tex]To find the 18th terem, substitute n = 18 into the nth term
[tex]\begin{gathered} T_{18}=52-10(18) \\ =52-180 \\ =-128 \end{gathered}[/tex]