Question

i am having a hard time understanding the number sequence on iductive reasoning. the question is to predict next three numbers in the sequence 1,4,9,16....

Answer 1

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Answer 2

what can you tell me about the number 4?

Answer 3

what are its factors?

Answer 4

2
4,6,8,

Answer 5

how are 6,8 factors of 4?

Answer 6

its 25 36 and 49

Answer 7

that was a type o

Answer 8

okay. do you see that 4 is 2 times 2?

Answer 9

they r squares

Answer 10

yes@dhatraditya

Answer 11

If you happen to see that 1,4,9,16 ... is 1^2, 2^2, 3^2, 4^2, then it's easy to figure out the next few terms. But what do you do if you don't see it? Is there something else you can try? The answer is yes. You create another sequence from the original sequence in the hope that the pattern is easier to spot in the new sequence. You then use that information to figure out how the original sequence should continue. So here's what you do ... from the original sequence of 1, 4, 9, 16, ... subtract the first term from the second term, then subtract the second term from the third term, then subtract the third term from the fourth term, etc. If you do this, the new sequence you get is 3, 5, 7. The pattern in this new sequence should be obvious. Next should be 9, 11, 13, etc. We now go back to our original seqence and derive the next 3 terms. We add 9 to 16 to get 25. We then add 11 to 25 to get 36. And then we add 13 to 36 to get 49. Picture it this way :

1 4 9 16 25 36 49
\ / \ / \ / \ / \ / \ /
3 5 7 9 11 13