Question

Write a rule for the nth term of the arithmetic sequence with a7=1 and a2=26

Answer 1

$a_7=1;\ a_2=26\\\\a_n=a_1+(n-1)d\\\\a_7-a_2=5d\to5d=1-26\to5d=-25\to \boxed{d=-5}\\\\a_1=a_2-d\to a_1=26-(-5)=26+5=\boxed{31}\\\\\boxed{a_n=31+(n-1)\cdot(-5)=31-5n+5=\boxed{36-5n}}$