Question

1,2,5,12,23 general term ???

Answer 1

Before going on to look at harder examples, we list some of the important sequences that you should know:

1, 3, 5, 7, 9, 11, 13, ...

the odd numbers un = 2n – 1

2, 4, 6, 8, 10, 12, 14, ...

the even numbers un = 2n

1, 4, 9, 15, 25, 36, 49, ...

the square numbers un = n2

1, 8, 27, 64, 125, 216, 343, ...

the cube numbers un = n3

1, 3, 6, 10, 15, 21, 28, ...

the triangular numbers un =
1
2
n(n + 1)

There is one other important sequence, namely the prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...

Note: there is no formula for calculating the nth prime number.
We now look at other, harder sequences generated by algebraic rules.