Given:
The sequence is:
-15,-10,-4, 3, 11, ______
To find:
The next number.
Solution:
We have,
-15,-10,-4, 3, 11, ______
Here, the difference between two consecutive terms are:
[tex]-10-(-15)=-10+15[/tex]
[tex]-10-(-15)=5[/tex]
Similarly,
[tex]-4-(-10)=6[/tex]
[tex]3-(-4)=7[/tex]
[tex]11-3=8[/tex]
It is clear that the difference difference between two consecutive terms is increasing by 1. So, the next difference must be (8+1)=9.
Let the next number be x. Then,
[tex]x-11=9[/tex]
[tex]x=9+11[/tex]
[tex]x=20[/tex]
Therefore, the next number of the sequence is 20.
