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.