Answer:
There are 15 terms in the arithmetic sequence.
Step-by-step explanation:
Given: [tex]a_1=-3[/tex], [tex]a_n=18[/tex], [tex]d=\frac{3}{2}[/tex]
Find: [tex]n=?[/tex]
Formula: [tex]a_n=a_1+(n-1)d[/tex]
Solution:
[tex]a_n=a_1+(n-1)d\\18=-3+(n-1)\frac{3}{2}\\18=-3+\frac{3n}{2}-\frac{3}{2}\\(18\times2)=(-3\times2)+(\frac{3n}{2}\times2)-(\frac{3}{2}\times2)\\36=-6+3n-3\\3n=36+6+3\\3n=45\\\frac{3n}{3}=\frac{45}{3}\\\boxed{n=15}[/tex]
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