Question

Determine the 42nd term of the sequence 12.25, 14.50, 16.75

Answer 1

`a_1=12.25,\ a_2=14.50,\ a_3=16.75\\\\a_2-a_1=14.50-12.25=2.25\\a_3-a_2=16.75-14.50=2.25\\a_(n+1)-a_n=2.25=constans\\\\\text{It's an arithmetic sequence with}\\a_1=12.25,\ d=2.25\\\\a_n=a_1+(n-1)d\to a_n=12.25+(n-1)(2.25)=12.25+2.25n-2.25\\a_n=10+2.25n\\\\n=42\to a_(42)=10+2.25(42)=10+94.5=104.5\\\\Answer:\ \boxed{a_(42)=104.5}`