Find an equation for the general term of the given arithmetic sequence and use it to calculate its $$75^{th}$$ term: $$ 8,5,2,-3,−6,…$$

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Uniteasy Admin · Accepted Answer

Begin by finding the common difference,
$$d=5−8=−2$$
Next find the formula for the general term, here $$a_1=8$$ and $$d=−3$$.
$$a_n=a_1+(n-1)d$$
$$=8+(n-1)(-3) $$
$$= -3n+11$$
Therefore, $$a_n=-3n+11 $$and the $$ 75^{th} $$ term can be calculated as follows:
$$a_{75}=11-3	imes 75 =214$$

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