1,4,9,16. Check the differences between the differences (second difference).

3,5,7...there's the pattern: 3,5,7,9,11,13,15...

The next second difference is 9, thus the next difference is 16+9=25. 69-25=44.

99,98,94,85,69,44...
Answer by Cromlix(4381)   (Show Source): You can put this solution on YOUR website!
99 -> 98 decrease of 1^2
98 -> 94 decrease of 2^2
94 -> 85 decrease of 3^2
85 -> 69 decrease of 4^2
69 -> 44 decrease of 5^2
Therefore next number = 44.
Hope this helps.
:-)
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

First thing to do is recognize that this is not a series. It is a sequence.

is a series.

99  98  94  85   69    Starting with the 2nd term. Subtract each term from
   1   4   9   16      the term immediately to its left.
    -3  -5  -7         Repeat
       2   2           Stop here because the results of two adjacent subtractions were equal

Since the last row shows equal results, a 3rd element in that last row would have also been 2, so write that in

99  98  94  85   69     
   1   4   9   16       
    -3  -5  -7         
       2   2   2          

That 2 would have been the result of a previous subtraction, so put in a -9 i the row above

 99  98  94  85   69     
   1   4   9   16       
    -3  -5  -7   -9      
       2   2   2  

Then a 25 in the row above that, and finally put in the 44 (69 - 25) which is the desired next term.

 99  98  94  85   69  44   
   1   4   9   16   25     
    -3  -5  -7   -9      
       2   2   2