Question

Which term of the arithmetic sequence 2, 5, 8... is equal to 227?

Answer 1

`a_1=2;\ a_2=5;\ a_3=8;\ ...;\ a_n=227\\\\the\ difference\ d=a_2-a_1\\\\d=5-2=3\\\\a_n=a_1+(n-1)d\\\\subtitute\\\\a_n=2+(n-1)\cdot3=2+3n-3=3n-1\\---------------------\\\\3n-1=227\ \ \ |add\ 1\ to\ both\ sides\\\\3n=228\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{n=76}`

Answer: 76-th term is equal 227.