The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?

Guest Mar 4, 2021

#1**+1 **

difference d=−31/9.

We have that a5=9

This means that +d(5−1)=9 or a1+4d=9.

We have that a32=−84.

This means that a1+d(32−1)=−84 or a1+31d=−84.

We have that d=−319.

We obtained the following system:

a1+4d=9

a1+31d=−84

d=−31/9

Solving it, we obtain that a1=205/9, d=-31/9.

Finally,

a23=a1+d(23−1)=205/9+(−31/9)(23−1)=−53.

Charger421 Mar 4, 2021