Which number completes the sequence 3 9 4 5 25 20 21 441?

Answer 1

436 is the best choice for the next number in the sequence because:

• 3x3=9-5=4
• 5x5=25-5=20
• 21x21=441-5=436

The Pattern: Square the term, then take away 5, add one, and square it again, and so on.

Answer 2

Un = (Un-1)2 for n = 3k+1

Un = Un-1 - 5 for n = 3k+2

Un = Un-1 + 1 for n = 3k

In other words,

• square the previous number
• subtract 5 from the previous number
• add 1 to the previous number
• repeat.

Answer 3

436.

One possible sequence is Square, -5, +1, Sq, ...

Answer 4

None. "Complete" implies that the number you are seeking is the LAST one: there can be no more after it. The sequence given above can be continued infinitely and so cannot be completed.

Answer 5

436