Question

The first term of an arithmetic sequence is -5, and the tenth term is 13. find the common difference. use the common difference to find the 18th term in the sequence.

Answer 1

$a_1=-5;\ a_{10}=13;\ d=?;\ a_{18}=?\\\\a_{10}-a_1=9d\\\\subtitute\\\\9d=13-(-5)\\9d=13+5\\9d=18\ \ \ |divide\ both\ sides\ by\ 9\\\boxed{d=2}\\\\a_{18}=a_{10}+8d\\\\subtitute\\\\a_{18}=13+8\cdot2\\a_{18}=13+16\\\boxed{a_{18}=29}\\\\\\Answer:\boxed{d=2\ and\ a_{18}=29}$