NMT / ZNO

Formulas and reference

A compact mathematics reference in two levels: the NMT exam sheet and the full ZNO formula set.

ZNO — full reference · Algebra · 8 formulas
Full ZNO Expanded school formula set. The “NMT” badge marks formulas also present on the compact sheet.
Sequences

Arithmetic progression

n-th term of an arithmetic progression

NMT
\[a_n=a_1+d(n-1)\]
9–11 grade

Sum of the first n terms of an arithmetic progression

NMT
\[S_n=\frac{a_1+a_n}{2}\,n\]
9–11 grade

Sum in terms of a₁ and d

\[S_n=\frac{2a_1+d(n-1)}2\,n\]
9–11 grade

Property of an arithmetic progression

\[a_n=\frac{a_{n-1}+a_{n+1}}2\]
9–11 grade
Sequences

Geometric progression

n-th term of a geometric progression

NMT
\[b_n=b_1q^{\,n-1}\]
9–11 grade

Sum of the first n terms of a geometric progression

NMT
\[S_n=\frac{b_1(q^n-1)}{q-1}\]
Condition \(q\ne1\)
9–11 grade

Sum of an infinite geometric progression

\[S=\frac{b_1}{1-q}\]
Condition \(|q|\lt 1\)
9–11 grade

Property of a geometric progression

\[b_n^2=b_{n-1}b_{n+1}\]
9–11 grade