What is the next number in the sequence?
1,2,4,7,11,16,22,?
The increases from one number to its next is follows the pattern
1, 2, 3, 4, 5, ....
So it should be easy to see that the next number is 22+7 = 29
on a next higher level of the study of these, you will be asked to
find the expression for any term(n), where n is the term number
You will learn that the above sequence is quadratic and learn several
methods to find the defining function.
1, 1, 3, 7, 13, 21, 31, ?
after playing around a bit with these ...
...
...
3 = 1x2 + 1
7 = 2x3 + 1
13 = 3x4 + 1
21 = 4x5 + 1
31 = 5x6 + 1
mmmhhhh?
how about
t(n ) = (n-2)(n-1) + 1
does not work for t(1) so it must be defined as t(1) = 1
testing for t(7) = (5)(6) + 1 = 31 , ok then!
t(n) = (n-2)(n-1) +1, where t(1) = 1 , and n > 1, with n ∊ N
Uh I don't get it
To find the next number in the sequence, we need to look for a pattern.
If we observe the differences between consecutive terms, we get:
2 - 1 = 1,
4 - 2 = 2,
7 - 4 = 3,
11 - 7 = 4,
16 - 11 = 5,
22 - 16 = 6.
So, the differences between the terms are increasing by 1 each time.
Based on this pattern, we can infer that the next difference should be 7. So, we add 7 to the last term, 22, to get the next term in the sequence.
22 + 7 = 29.
Hence, the next number in the sequence is 29.