Answer to Question #20562 in Algebra for fardowsa

Question

what is the nth term for this sequence?
7, 18, 35, 58, 87, 122

Answer 1

we can consider differences
18-7=11
35-18=17
58-35=23
87-58=29
122-87=35 if a1=7 then a2=7+11
a3=a2+11+6=7+11+11+6=a1+2*11+6
a4=a3+11+2*6 so a_n=a_(n-1)+11+(n-2)*6
or a_n=a1+(n-1)*11+(1+2+...+(n-2))*6=a1+11*(n-1)+(n-1)*(n-2)*6/2=
=a1+11(n-1)+3(n-1)*(n-2)=7+11n-11+3(n^2-3n+2)=11n-4+3n^2-9n+6=3n^2+2n+2, for
n>=2 so a1=7, an=3n^2+2n+2, but for n=1 a1=3*1^2+2*1+2=7 sofor every n a_n=3n^2+2n+2