can anybody help me find the pattern in these two sequences please!! I can find the next two terms after that myself. I have spent at least 30 minutes on each and I can't figure it out...help!!
1)1, 1/4, 1/9, 1/16, 1/25,....
2)1, 1/2, 1/3, 1/4,....
the pattern appears to be quite obvious
1, 1/4, 1/9, 1/16, 1/25,.... or
1/1^2, 1/2^2, 1/3^2,1/4^2 etc
the second is even more obvious.
doesn't the denominator start at 1 and increase by 1 ??
In case you didn't understand Reiny's answer for the first problem --
1 = 1 divided by 1 squared
1/4 = 1 divided by 2 squared
1/9 = 1 divided by 3 squared
1/16 = 1 divided by 4 squared
1/25 = 1 divided by ? squared
?? = 1 divided by 6 squared
I'm sure you can find the next number in this sequence.
1/34
Of course, I'll be happy to help you find the patterns in these sequences!
1) The first sequence is: 1, 1/4, 1/9, 1/16, 1/25,....
To find the pattern in this sequence, we can observe that each term is the reciprocal of a perfect square. Specifically, each term is the reciprocal of the square of its respective position.
For example, the first term 1 is the reciprocal of 1^2, the second term 1/4 is the reciprocal of 2^2, the third term 1/9 is the reciprocal of 3^2, and so on.
Therefore, the pattern in this sequence is that each term is the reciprocal of the square of its position.
To find the next two terms, you can continue the pattern. The next term would be the reciprocal of 6^2, which is 1/36, and the term after that would be the reciprocal of 7^2, which is 1/49.
So, the next two terms in the sequence are 1/36 and 1/49.
2) The second sequence is: 1, 1/2, 1/3, 1/4,....
To find the pattern in this sequence, we can observe that each term is the reciprocal of its position.
For example, the first term 1 is the reciprocal of 1, the second term 1/2 is the reciprocal of 2, the third term 1/3 is the reciprocal of 3, and so on.
Therefore, the pattern in this sequence is that each term is the reciprocal of its position.
To find the next two terms, you can continue the pattern. The next term would be the reciprocal of 5, which is 1/5, and the term after that would be the reciprocal of 6, which is 1/6.
So, the next two terms in the sequence are 1/5 and 1/6.
I hope this helps! Let me know if you have any further questions.