Answer: $345
Step-by-step explanation:
The explicit rule for an arithmetic sequence is: [tex]a_n=a_1+d(n-1)\ \text{where}\ a_1\ \text{is the first term and d is the difference}[/tex]
In the given problem, [tex]a_1=12[/tex] and d = 5
[tex]a_n=12+5(n-1)\\.\quad=12+5n-5\\.\quad=5n+7\\\\a_{10}=5(10)+7\\.\quad=50+7\\.\quad=57[/tex]
The sum of an arithmetic sequence is: [tex]S_n=\dfrac{a_1+a_n}{2}\cdot n[/tex]
[tex]S_{10}=\dfrac{12+57}{2}\cdot 10\\\\.\quad=69\cdot 5\\\\.\quad=345[/tex]
