Answer
a(n) = 60n + 20
a(100) = 6020
Step-by-step explanation:
Given the following sequences
80, 140, 200
[tex]\begin{gathered} \text{The given sequence is }80,\text{ 140, 200} \\ \text{Step 1: find the common difference} \\ \text{common difference= next term - previous term} \\ \text{Common difference = 140 - 80} \\ \text{Common difference = 60} \\ \text{common difference = 200 - 140} \\ \text{common difference = 60} \\ \text{Hence, the common difference is 60} \\ \text{The nth term of an arithmetic progression is} \\ a(n)\text{ = a + (n - 1) x d} \\ \text{where a = first term, n = no of terms, and d = common difference} \\ a(n)\text{ = 80 + (n - 1) x 60} \\ \text{open the parenthesis} \\ a(n)\text{ = 80 + 60n - 60} \\ a(n)\text{ = 60n + 80 - 60} \\ a(n)\text{ = 60n + 20} \\ \\ \text{ Find the 100th term} \\ \text{let n = 100} \\ a(100)\text{ = 60(100) + 20} \\ a(100)\text{ = 6000 +2}0 \\ a(100)\text{ = 6020} \end{gathered}[/tex]
