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make a conjecture as to what number comes is next
-15,-10,-4, 3, 11, ______

Sagot :

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.

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