The general term for the sequence 2, 4, 6, 8, 10 can be represented as:
a(n) = 2n
This means that for any positive integer n, if you multiply n by 2, you will get the nth term in the sequence. For instance:
- For n = 1, a(1) = 2 × 1 = 2
- For n = 2, a(2) = 2 × 2 = 4
- For n = 3, a(3) = 2 × 3 = 6
- For n = 4, a(4) = 2 × 4 = 8
- For n = 5, a(5) = 2 × 5 = 10
As we can see, this formula consistently generates each term in the sequence. Thus, the expression 2n effectively captures the pattern of the sequence.