Question

find a(n) for the arithmetic sequence

a(12)=7,a(14)=15

Answer 1

a(n) = a(n-1) + d
(15 = a(14) + d)
subtract
(7 = a(12) + d)
8 = 2a, divide by 2, a = 4

now you have y = 2(n-1) + d, and
7 = 2(12) + d, --> 7 = 24 + d, subtract 24,
d = -17

So now you have a = 2, d = -17
a(n) = 2(n-1) - 17