Question

Write an explicit formula for the sequence 7,2,-3,-8,-13... then find the 14th term

Answer 1

The series of these numbers are arithmetic progression because every time you subtract the next term to the previous term, each difference is common (or constant), that 2 - 7 = -5, or -3 - 2 = -5.

You can use the formula of the arithmetic term, that is
an = a1 + (n - 1)d
where an = nth term, a1 = first term, n = number of terms, d = common difference

The 14th term will be
a(14th term) = 7 + (14 - 1)*(-5) = -58