How menu terms are in the arithmetic sequence 7,0,-7, ...,-175?

27 terms

Step-by-step explanation:

Here the first term is 7 and the common difference is - 7. Each new term is equal to the previous term, less 7.

The general formula that involves first and last terms, common difference and number of terms is last = first + (n - 1) (common difference)

We substitute the knowns, as follows:

-175 = 7 + (n-1) (-7)

Solve this first for n-1, and then for n:

Subtract 7 from both sides: - 182 = - 7 (n-1)

Dividing both sides by - 7 yields 26 = n - 1

Then n = 27.

There are 27 terms in this arith. sequence.