Use the principle of mathematical induction to show that the mathematical statement is true for all natural numbers n.Sn: 1 + 4 + 7 + . . . + (3n - 2) = 
What will be an ideal response?
| S1: | 1   |
1 = 1 ?
Sk: 1 + 4 + 7 + . . . + (3k - 2) =
Sk+1: 1 + 4 + 7 + . . . + (3k + 1) =
We work with Sk. Because we assume that Sk is true, we add the next consecutive term, namely
3(k+1) - 2, to both sides.
1 + 4 + 7 + . . . + (3k - 2) + (3(k + 1) - 2) =
+ (3(k + 1) - 2)1 + 4 + 7 + . . . + (3k + 1) =
+ (3k + 1)1 + 4 + 7 + . . . + (3k + 1) =
+ 
1 + 4 + 7 + . . . + (3k + 1) =
1 + 4 + 7 + . . . + (3k + 1) =
We have shown that if we assume that Sk is true, and we add 3(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.
Mathematics
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