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 $95.$