Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 4 + 9 + 14 + . . . + (5n - 1) = 
What will be an ideal response?
| S1: | 4   |
4 = 4 ?
Sk: 4 + 9 + 14 + . . . + (5k - 1) =
Sk+1: 4 + 9 + 14 + . . . + (5k + 4) =
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
5(k+1) - 1, to both sides.
4 + 9 + 14 + . . . + (5k - 1) + (5(k + 1) - 1) =
+ (5(k + 1) - 1)4 + 9 + 14 + . . . + (5k + 4) =
+ (5k + 4)4 + 9 + 14 + . . . + (5k + 4) =
+ 
4 + 9 + 14 + . . . + (5k + 4) =
4 + 9 + 14 + . . . + (5k + 4) =
We have shown that if we assume that Sk is true, and we add 5(k+1) - 1 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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