Question

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

Answer 1

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