Which explicit rule is correct for the sequence (7,13,23,37,\ldots)?

Correct answer: (a_n=2n^2+5)

The governing concept is selecting an explicit rule by testing the pattern of differences. The first differences are 13−7=6, 23−13=10, and 37−23=14; these increase by 4, so the second difference is constant. A quadratic rule is therefore plausible. Test option A: for n=1, 2(1)^2+5=7; for n=2, 2(2)^2+5=13; for n=3, 2(3)^2+5=23; and for n=4, 2(4)^2+5=37. Thus option A reproduces every given term and is correct. Option B is linear and gives 14 at n=1, option C gives 7 initially but 10 at n=2, and option D gives 7 initially but has constant difference 6, so none matches the sequence.