You are having a discussion about sequences with your classmate. she insists the the sequence 2,3,5,8,12 must be either arithmatic or geometric. is she correct or incorrect? explain.

The sequence is, in fact, quadratic. It is described by the equation
.. a[n] = (n*(n -1))/2 +2

First differences are increasing, so the sequence will not be arithmetic. An arithmetic sequence has constant first differences.

Second differences are constant, so the sequence will not be geometric. A geometric sequence will have first-, second-, third-differences, and those to any level, that have the same constant ratio as the terms of the original sequence.

3were boys and 5 were girls