What is the next term in -2, -5, -9, -14, -20.
and why

The next term would be -27

Lets pretend that all the negative signs went away, that way you have the data:

2, 5, 9, 14, 20

^^^In my opinion it just makes it easier because I don't like negative numbers. Keep in mind that the negatives are still there but I just made them "Invisible"

The pic below is how I found the pattern. If you can't tell by the picture from 2 to 5 it increases by 3. From 5 to 9 it increases by 4. From 9 to 14 it increases by 5. From 14 to 20 it increases by 6.

This means the pattern is to increase the number 1 more then the amount the previous number was increased (keep in mind this is the pattern for the positive version and therefore the original pattern would be decreasing (since the bigger a number that is negative is, the farther away it gets from zero, therefor getting smaller.) For the original version the rule would be: it would decrease the number 1 more then the amount the previous number was decreased) <<<Hope that makes sense

That means that 20 will be increased by 7 ( 6+ 1 = 7). Which equals 27. Make the negative sign visible again and your answer is -27.

Let me know if this made sense and if it was helpful!

hi,

you half the rectangle that you ae asking about so then you would see the scale factor of 1/2 the one u have selected, the one on top is half.

hope this !