Question

Given that t 8 = 60 and t 12 = 48, find the 45th term of the arithmetic sequence.

Answer 1

`t_8=60\\t_(12)=48\\t_(45)=?\\\\\t_n\ \text{It's an arithmetic sequence, therefore the difference d we can calculate:}\\\\4d=t_(12)-t_8\\\\4d=48-60\\4d=-12\ \ \ \ |:4\\d=-3\\\\t_(45)=t_(12)+33d\to t_(45)=48+33\cdot(-3)=-51`
Answer: 45th term is equal -51.