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An arithmetic sequence with a third term of 8 and a constant difference of 5.

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An arithmetic sequence (a_n) is as follows:


a_1\\a_2=a_1+d\\a_3= a_1+2d\\a_4=a_1+3d,... where
a_1 is the first term and d is the constant difference,

thus, we see that the n'th term of an arithmetic sequence is
a_n=a_1+(n-1)d


in our particular case d=5, the third term is 8, so we have:


a_3=8=a_1+2\cdot5\\\\8=a_1+10\\\\a_1=-2


and the general term is
a_n=-2+5(n-1),


Answer: first term is -2, n'th term is -2+5(n-1)


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