Series And Sequences, U"1,16,81,256,625 Whats Next?Need Help Please"

Series and Sequences

1,16,81,256,625 whats next?need help please

Answer:

Step-by-step explanation:

Square roots:

√1 = 1

√16 = 4

√81 = 9

√256 = 16

√625 = 25

The consecutive roots of the given sequence are 1, 4, 9, 16, 25.

Difference between consecutive roots:

4-1 = 3

9-4 = 5

16-9 = 7

25-16 = 9

The difference are consecutive odd numbers 3, 5, 7, 9.

The next odd difference is 11.

Add 11 to last root of the sequence.

√625 + 11

= 25 + 11

= 36

Therefore the next sequence is the square of 36.

36² = 1,296.

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