Answer to Question #297191 in Algebra for Victoria

Question

How many terms are there for the arithmetic sequence

28 , 25 , 22 , 19 , ⋯ , − 29 , − 32 ?

Answer 1

$$a_1=28, d=a_2-a_1=25-28=-3$$

The n-th term of the arithmetic sequence is

$$a_n=a_1+d(n-1)$$

$$a_n=28-3(n-1)=-32$$

$$3(n-1)=60$$

$$n-1=20$$

$$n=21$$

There are 21 terms in the given arithmetic sequence.