A (1) = - 2 a (n) = a (n - 1) - 5 Find the 4 ^ (th) term in the sequence.

-17

Step-by-step explanation:

Each term in the sequence is 5 less than the one before, so the first 4 terms are ...

-2, - 7, - 12, - 17

The 4th term of the sequence is - 17.

__

The general term (an) of the sequence can be written as ...

an = a1 + d (n - 1)

where a1 is the first term and d is the common difference. Here, those are ...

a1 = - 2, d = - 5

so the general term is ...

an = - 2 - 5 (n - 1)

We can use this to find the 4th term:

a4 = - 2 - 5 (4 - 3)

a4 = - 17