What Is the Next Number in This Mathematical Sequence?

[cjbreen]

What is the next number in the sequence? 2, 3, 10, 15, 26, 35, 50, ?

 

[cristo]

Is this some sort of homework question?

 

[it.anoopk]

63
1st..(1*1)+1 odd
2nd (2*2)-1 even
3rd (3*3)+1 odd
...
8th (8*8)-1 even

 

[nabeelr]

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.

 

[WHOAguitarninja]

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.

 

[alexk174]

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

 

[alexk174]

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...

 

[alexk174]

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

 

[leopard]

10 10 11 12 15 16 21

 

[unscientific]

S_(n) = 2, 3, 10, 15, 26, 35, 50, 63, ... , (n²) - (-1)ⁿ


T_(n) = (n²) - (-1)ⁿ