Question

PLZ ANSWER FAST In an arithmetic sequence, a17 = -40 and a28 = -73. explain how to use this information to write a recursive formula for this sequence.

Answer 1

`a_(r+1)=a_r-3`

Explanation:

`Let\ first\ term=a\\\\Let\ constant\ difference=d\\\\n^(th)\ in Arithmetic\ sequence\ is\ given\ by\ a_n=a+(n-1)d\\\\a_(17)=-40\\\\a_(17)=a+(17-1)d\\\\a+16d=-40................eq(1)\\\\a_(28)=-73\\\\a_(28)=a+(28-1)d\\\\a+27d=-73.................eq(2)\\\\eq(1)-eq(2)\\\\a+16d-a-27d=-4-+73\\\\-11d=33\\\\d=-3\\\\`

`a_(r+1)=a+(r+1-1)d\\\\a_(r+1)=a+r* d\\\\a_(r+1)=a+r* (-3)\\\\a_(r+1)=a-3r.................................eq(3)\\\\a_r=a+(r-1)d\\\\a_r=a+(r-1)* (-3)\\\\a_r=a-3r+3...................................eq(4)\\\\eq(3)-eq(4)\\\\a_(r+1)-a_r=(a-3r)-(a-3r+3)\\\\a_(r+1)-a_r=a-3r-a+3r-3\\\\a_(r+1)-a_r=-3\\\\a_(r+1)=a_r-3\\\\Required\ recursive\ formula:\ a_(r+1)=a_r-3`