Write an explicit formula for the nth term of the sequence -2/11, 3/13, -4/15, 5/17, -6/19.

1. Treat sign, numerator and denominator as three separate patterns. 2. The first term is negative and the second positive, so a factor of (-1)^n gives the right sign at every position. 3. The numerators are 2, 3, 4, 5, 6, which is n + 1 for n = 1, 2, 3, 4, 5. 4. The denominators are 11, 13, 15, 17, 19, rising by 2 each step, so they are 2n + 9. 5. Putting the three together gives a_n = (-1)^n (n + 1) / (2n + 9). 6. Testing n = 1 gives -2/11, which matches, while 2n + 7 gives 9 and 2n + 11 gives 13 at n = 1, so both fail the test. 7. A numerator of n + 2 would give 3 at n = 1, so that option fails as well. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 Sequences and Their Notations_