Answer to Question #160396 in Algebra for Annie

Question

The fifth term in an arithmetic sequence is 110 and the seventeenth term is 74. Find the tenth term in the sequence.

Answer 1

Given an arithmetic sequence

$$a_5=a+4d=110$$

$$a_{17}=a+16d=74$$

Then

$$a+16d-(a+4d)=74-110$$

$$12d=-36$$

$$d=-3$$

Find $a$

$$a+4(-3)=110$$

$$a=122$$

Hence

$$a_{10}=a+9d=122+9(-3)=95$$

The tenth term in the sequence is $95.$