Question

How do you complete the statement for the arithmetic sequence: -14 is the __ term of 2 1/5, 2, 1 4/5,...?

Answer 1

82nd

Explanation:

We know that the nth term of an arithmetic sequence is given by `t_n = a + (n - 1)d`. Our first term is `2 1/5 = 11/5` and our common difference is `-1/5`.

`-14 = 11/5 + (n - 1)-1/5`

`-14 = 11/5 - 1/5n + 1/5`

`-14 = 12/5 - 1/5n`

`-14 - 12/5 = -1/5n`

`-82/5 = -1/5n`

`n = (-82/5)/(-1/5)`

`n = 82`

Hopefully this helps!