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