SOLUTION: Find the 25th term in the sequence 0, 3, 8, 15, 24, 35, ..........

Question 1049661: Find the 25th term in the sequence 0, 3, 8, 15, 24, 35, ..........

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Find the 25th term in the sequence , , , , ,, ..........
The sequence of differences is:
, .....,..... ,..... ,..... ,.....,
.....................................->first differences consecutive odd numbers
.....................................->second differences same, so no need to go further
I happen to know that the sum of consecutive odd numbers is a square:

.....and so on.
The formula for this is
+ ... +
Your sequence is just my sum with removed from the start! So the
formula is:
(for all terms given)

then the 25th term in the sequence is:

here it is:
{0, 3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143, 168, 195, 224, 255, 288, 323, 360, 399, 440, 483, 528, 575, , 675, 728, 783, 840, 899, 960, 1023, 1088, 1155, 1224, 1295, 1368, 1443}....

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