The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term? HELP PLEASE!!!
+307 Answer: \(-53\)
The common difference is \(-84-9\over32-5\), which is -93/27, or \(-3\frac49\).
This means that the 23rd term is 9 \(-3\frac49\)(23-5), which is \(-53\).
Edit: I forgot to add an explanation for anything, and I'm low on time right now. See if you can understand the following:
The common difference is the \(n_{2}-n_{1}\over t_{2}-t_{1}\), where t is the term number (\(t_2\) being farther in the sequence) and \(n_{2}\) being the number that \(t_{2}\) is, and same with \(n_{1}\)and \(t_{1}\). The xth term will be \(n_{1}\)+ the common difference x (x - \(t_{1}\)).
So basically the formula for any question like that, if I am thinking correctly, and assuming all the variable are as meantioned earlier in the eplanation is:
\(n_{1}+\)\(n_{2}-n_{1}\over t_{2}-t{1} \)\(\cdot (x-t_{1})\).
