Question

find an equation for the nth term of the arithmetic sequence. a14 = -33, a15 = 9 select one: a. an = -579 42(n 1) b. an = -579 42(n - 1) c. an = -579 - 42(n 1) d. an = -579 - 42(n - 1)

Answer 1

`The\ arithmetic\ sequence:a_n=a_1+(n-1)d\\\\a_(14)=-33;\ a_(15)=9\\\\a_(15)-a_(14)=d\\\\d=9-(-33)=9+33=42\\\\a_1=a_(14)-13d\\\\a_1=-33-13\cdot42=-33-546=-579\\\\\boxed{a_n=-579+42(n-1)}`