Question

Use inductive reasoning to predict the next line in the sequence of computations.

1 = 1 x 1
1 + 7 = 2 x 4
1 + 7 + 13 = 3 x 7

Answer 1

On the left, we have an increase of 6. On the right, we have an increase of one and the corresponding multiplication:
1 = 1 × n
1 + (1+6) = 2 × n
1 + (1+6) + (1+6+6) = 3 × n

Therefore, the next line should be:
1 + (1+6) + (1+6+6) + (1+6+6+6) = 4 × n
which is:
1 + 7 + 13 + 19 = 4 × 10

Because 1 + 7 + 13 + 19 = 40
And 40 = 4 × 10