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

 Jul 12, 2021

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:


\(n_{1}+\)\(n_{2}-n_{1}\over t_{2}-t{1} \)\(\cdot (x-t_{1})\).

 Jul 13, 2021

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