PROBLEM:
What is the nth term of the sequence -3, -2, -1, 0?
SOLUTION:
[tex]\blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
• We can find the nth term or what we call the rule for the given sequence using the formula [tex] \tt a_n=a_1+(n-1)d[/tex] since the given sequence is an arithmetic one.
• First, we need to identify the value of the first term and the common difference. The value of the first term is -3. The common difference can be obtained when you subtract a term by its preceding term.
[tex] 0 - ( - 1) = 1[/tex]
[tex] - 1 - ( - 2) = 1[/tex]
[tex] - 2 - ( - 3) = 1[/tex]
> Thus, the common difference is 1.
[tex]\blue {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: }}[/tex]
• Using the formula, we'll have:
[tex] \large \begin{array}{l}\tt a_n=a_1+(n-1)d \\ \tt a_n= - 3+(n-1)1 \\ \tt a_n= - 3 + n - 1 \\ \tt a_n=n - 4\end{array}[/tex]
ANSWER:
The nth term for the given arithmetic sequence is [tex] \tt n -4.[/tex]
