Series

Cards (7)

  • Arithmetic nth term
    un=u_n= a+a+(n1)d\left(n-1\right)d
  • Arithmetic sum
    Sn=S_n= n2(2a +(n1)d)\frac{n}{2}\left(2a\ +\left(n-1\right)d\right)
    Sn=S_n= n2(a + L)\frac{n}{2}\left(a\ +\ L\right) where a is the first term and L is the last term
  • Geometric nth term
    un=u_n= arn1ar^{n-1}
  • Geometric sums
    Sn=S_n= a(1rn)1r\frac{a\left(1-r^n\right)}{1-r}
    S=S_{\infty}= a1r\frac{a}{1-r}
  • It's an increasing sequence if un+1>unu_{n+1}>u_n for all n
  • It's a decreasing sequence if un+1<unu_{n+1}<u_n for all n
  • It's a period sequence if un+k=u_{n+k}=unu_n for all n and its period/order is k