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

Answer:

$a_{r+1}=a_r-3$

Step-by-step explanation:

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

$a_{r+1}=a+(r+1-1)d\\\\a_{r+1}=a+r\times d\\\\a_{r+1}=a+r\times (-3)\\\\a_{r+1}=a-3r.................................eq(3)\\\\a_r=a+(r-1)d\\\\a_r=a+(r-1)\times (-3)\\\\a_r=a-3r+3...................................eq(4)\\\\eq(3)-eq(4)\\\\a_{r+1}-a_r=(a-3r)-(a-3r+3)\\\\a_{r+1}-a_r=a-3r-a+3r-3\\\\a_{r+1}-a_r=-3\\\\a_{r+1}=a_r-3\\\\Required\ recursive\ formula:\ a_{r+1}=a_r-3$