What Is the Next Number in This Mathematical Sequence?

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In summary, the next number in the sequence is 63, and the pattern can be represented by the formula T(n) = (n2) - (-1)n. This was found by calculating the differences between the numbers in the sequence and taking the sum of the last two digits in the first set and subtracting the first digit, then repeating the process with the second set. Another method used was adding or subtracting values from each number in the sequence to get the next number.
  • #1
cjbreen
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What is the next number in the sequence? 2, 3, 10, 15, 26, 35, 50, ?
 
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  • #2
Is this some sort of homework question?
 
  • #3
63
1st..(1*1)+1 odd
2nd (2*2)-1 even
3rd (3*3)+1 odd
...
8th (8*8)-1 even
 
  • #4
yeah i got 63 too, but in a different way i think.
basically, the differences between them respectively, are 1, 7, 5, 11, 9, and 15.
divide it like this: 1, 7, 5, and 11, 9, 15
then take the sum of the last two digits in the first set, and subtract the first. so in this case, 7 + 5 -1.
you get 11, which is the next difference.
do this with the second set of 11, 9, and 15 and you'll get 13 as the next difference, meaning that 50 + 13 should be the next number.
that's how i got 63.
let me know what you guys think.
 
  • #5
nabeelr said:
yeah i got 63 too, but in a different way i think.
basically, the differences between them respectively, are 1, 7, 5, 11, 9, and 15.
divide it like this: 1, 7, 5, and 11, 9, 15
then take the sum of the last two digits in the first set, and subtract the first. so in this case, 7 + 5 -1.
you get 11, which is the next difference.
do this with the second set of 11, 9, and 15 and you'll get 13 as the next difference, meaning that 50 + 13 should be the next number.
that's how i got 63.
let me know what you guys think.

This is what I was thinking as well. I suspect it.anoopk's solution was probably the original intention. Seems a bit less random.
 
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  • #6
i got 63, too, but a different way, i got it by 2+1=3, add 6 to the one, 3:7=10, subtract 2 from the 7, add the number you grt<5> 15, add the 6 to 5 get 11 add 11 get 26 subtract 2 get 9 add 9 get 35 add 6 get 15 add 15 to 35 get 50 subtract 2 get 13 add 13 to 50 get 63 yay i win
 
  • #7
i got it a different way: =2+1=3 add 6 to 1 get 7 add 7 get 10 subtract 2 get 5 add 5 get 15 add 6 get 11 add 11 get 26 subtract 2 get 9 add 9 get 35 add 6 get 15 add 15 get 50 subtract to add 13 get 63 =[] this is the immature way to do it but i got it done in 3 minutes and I am only 12...
 
  • #8
alexk174 said:
i got it a different way: =2+1=3 add 6 to 1 get 7 add 7 get 10 subtract 2 get 5 add 5 get 15 add 6 get 11 add 11 get 26 subtract 2 get 9 add 9 get 35 add 6 get 15 add 15 get 50 subtract to add 13 get 63 =[] this is the immature way to do it but i got it done in 3 minutes and I am only 12...
that was too easy
 
  • #9
10 10 11 12 15 16 21
 
  • #10
S(n) = 2, 3, 10, 15, 26, 35, 50, 63, ... , (n2) - (-1)n


T(n) = (n2) - (-1)n
 

FAQ: What Is the Next Number in This Mathematical Sequence?

What is the purpose of finding the next number in a sequence?

The purpose of finding the next number in a sequence is to identify the pattern or rule that governs the sequence and use it to predict the next number in the sequence. This can be useful in various fields such as mathematics, statistics, and computer science.

How do you determine the rule or pattern in a sequence?

To determine the rule or pattern in a sequence, you can look for recurring numbers, differences between consecutive numbers, or any other noticeable patterns. You can also use algebraic equations or geometric shapes to represent the sequence.

Can there be multiple solutions for the next number in a sequence?

Yes, there can be multiple solutions for the next number in a sequence depending on the complexity of the sequence and the pattern or rule used to generate it. In some cases, there may be multiple valid solutions, while in others, there may be no clear pattern or rule.

What are some real-life applications of finding the next number in a sequence?

Finding the next number in a sequence has several real-life applications, such as predicting stock market trends, forecasting weather patterns, and analyzing consumer spending habits. It is also used in cryptography to generate secure keys and in data compression algorithms.

Is there a formula or method to find the next number in a sequence?

There is no one formula or method that can be applied to all sequences to find the next number. However, there are various mathematical techniques, such as arithmetic and geometric progressions, that can be used to find the next number in specific types of sequences. It ultimately depends on the complexity and nature of the sequence.

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