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

Guest Oct 1, 2017

#2**+1 **

We have that

a_{1} + 4d = 9 and

a_{1} + 31d = -84 where a_{1} is the first term and d is the common difference between terms

Subtract both equations

- 27d = 93 divide both sides by -27

d = - 93 / 27 = -31/ 9

And.....there are 18 terms between the 5th term and the 23rd term......so we have....

9 + 18(-31 / 9) = 9 - 62 = -53 = 23rd term

CPhill Oct 1, 2017

#2**+1 **

Best Answer

We have that

a_{1} + 4d = 9 and

a_{1} + 31d = -84 where a_{1} is the first term and d is the common difference between terms

Subtract both equations

- 27d = 93 divide both sides by -27

d = - 93 / 27 = -31/ 9

And.....there are 18 terms between the 5th term and the 23rd term......so we have....

9 + 18(-31 / 9) = 9 - 62 = -53 = 23rd term

CPhill Oct 1, 2017