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}`