Question

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

Answer 1

Answer:

1 + (1+6) + (1+6+6) + (1+6+6+6) = 4 × n

Step-by-step explanation:

The computation of the next line in the sequence is shown below:

As we can see that there is an increase of 6 in the left side and on the right hand side there is an increase of one

So,

1 = 1 × n

1 + (1+6) = 2 × n

1 + (1+6) + (1+6+6) = 3 × n

So, the next line would be  

1 + (1+6) + (1+6+6) + (1+6+6+6) = 4 × n

i.e.

1 + 7 + 13 + 19 = 4 × 10

As 1 + 7 + 13 + 19 = 40

And 40 = 4 × 10