Given the sequence: 8, 11, 14, 17,…, determine the 84th term and the sum of the first 59 terms.

It can be seen that the difference or subtraction between two successive terms of the sequence is always equal to 3.

 11-8 = 3.
 14-11 = 3.
 This means that the following term is always equal to the previous term plus three.
 Knowing this you can draw a formula or "rule" for succession.
 Assuming that the term 0 or X0 of the sequence is 8, then:
 
 X (n) = 8 + 3n.
 So, the term 84 is:
 X (84) = 5 + 3 * (84).
 X (84) = 260.
 The series would be:
 ∑  8 + 3x. from x=0 to x=59
 The result of that sum is: 5790