Transcript 3, 6, 11, 18, ... The first four terms of a sequence are shown above.

3, 6, 11, 18, ...
The first four terms of a sequence are shown above. Which of the following could
be the formula that gives the nth term of this sequence for all positive
integers n?
a) 2n
b) 2n + 1
c) 3n
d) n2 + 1
e) n2 + 2
e) n2 + 2
Explanation
If a formula gives the nth term of the sequence for all positive integers n, it must give
the nth term of the sequence for n = 1, 2, 3, and 4. If n = 1, then 2n = 2 and n2 + 1 =
2, but the first term of the sequence is 3, so the general formula cannot be 2n or n2 +
1. Also, if n = 3, then 2n + 1 = 7 and 3n = 9, but the third term of the sequence is 11,
so the general formula cannot be 2n + 1 or 3n. However, for n = 1, 2, 3, and 4, the
values of n2 + 2 are 3, 6, 11, and 18, respectively. Therefore, the general formula for
this sequence could be n2 + 2.