Use mathematical induction to prove that the statement is true for every positive integer n.3 + 8 + 13 + . . . + (5n - 2) = 
What will be an ideal response?
| S1: | 3   |
3 = 3 ?
Sk: 3 + 8 + 13 + . . . + (5k - 2) =
Sk+1: 3 + 8 + 13 + . . . + (5k + 3) =
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
5(k+1) - 2, to both sides.
3 + 8 + 13 + . . . + (5k - 2) + (5(k + 1) - 2) =
+ (5(k + 1) - 2)3 + 8 + 13 + . . . + (5k + 3) =
+ (5k + 3)3 + 8 + 13 + . . . + (5k + 3) =
+ 
3 + 8 + 13 + . . . + (5k + 3) =
3 + 8 + 13 + . . . + (5k + 3) =
We have shown that if we assume that Sk is true, and we add 5(k+1) - 2 to both sides of Sk, then Sk+1 is also true. By the principle of mathematical induction, the statement Sn is true for every positive integer n.
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