Question

Find an equation for the nth term of the arithmetic sequence.

a15 = -53, a16 = -5

Answer 1

an = -725 + 48(n - 1)

Answer 2

well you know

the general term is

\[a_{n} = a + (n - 1) \times d\]

a = 1st term, n = number of terms and d = common difference

well you know the difference between the 15th and 16th term is 48

so the common difference d = 48

substitute it to find a. I've used the 15th term

\[-53 = a + (15 -1) \times 48\]

so

-53 = a + 672

then a = -725

so the general term is

\[a_{n} = -725 + (n - 1) \times 48\]

you'll need to distribute the 48 and then collect like terms to get the final version of the general term.

hope this helps

Answer 3

thnx