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# HELP ASAPPPP

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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

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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