The square numbers can be defined by the recursive formula a1 = 1, and an = an-1 + (2n - 1), where n 1. The first five square numbers are?

A)1, 2, 2, 4, and 8.
B) 1, 3, 5, 7, and 9.
C) 1, 4, 9, 16, and 25.
D) 1, 5, 14, 30, and 55.

Question

The square numbers can be defined by the recursive formula a1 = 1, and an = an-1 + (2n - 1), where n > 1. The first five square numbers are?

A)1, 2, 2, 4, and 8.	
B) 1, 3, 5, 7, and 9.	
C) 1, 4, 9, 16, and 25.	
D) 1, 5, 14, 30, and 55.

mathwizzard3 · Answer

1, 4, 9, 16, and 25. Use the formula to get a2 = 1 + (2*2 - 1) = 4, a3 = 4 + (2*3 - 1) = 9, etc. Also notice that for all n, an = n2.

mathwizzard3 · Answer

Hope that helps! btw the answer choice for that would be C!