The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?
Let a be the first term, and r be the rate of the arithmetic sequence. We have:
a + 4r = 9
a + 31r = -84
a + 22 r = ?
Realize that we can Subtract our first equation from our second equation. This gives us:
27r = -93
r = -93/27
since we already have that a+31r = -84, we can just subtract 9r from this equation to get:
a + 22r = -84 -(9*-93/27) = -84 -(-31) = -84 + 31 = -53
Do u take algebra 2 classes at Santa Clara AOPS, because this looks like one of the homework questions.