Question

Calculate the next three numbers of each progression1) 15,-14,13,-12,11...2) 2,5,9,14...

Answer 1

1) We have the progression:

`15,-14,13,-12,11`

It seems that the absolute value is decreasing and one out of three terms have negative sign.

Then, we can continue the progression as:

`15,-14,13,-12,11,10,-9,8`

2) We have the progression:

`2,5,9,14`

We can calculate the difference between consecutive terms and see that it increases by one unit each step: 5-2=3, 9-5=4, 14-9=5.

Then the next term will be 6 units greater than 14.

Then 14+6=22.

The next term will be now 7 units greater than 22.

Then, 22+7=29.

The next term will be 8 units greater than 29, so 29+8=37.

We can write the sequence as:

`2,5,9,14,22,29,37`

Answer:

The next three terms are:

1) 10, -9, 8

2) 22, 29, 37