Grade 12 Mathematics Unit 1 : Sequences and Series

Sequences and series are the focus of Unit 1 of Grade 12 Mathematics in the Ethiopian (FDRE Ministry of Education) curriculum. First, it defines a sequence and its general term, then it studies arithmetic and geometric sequences and their patterns. After that, it writes sums with sigma notation and finds the partial sums of a series. Finally, it examines infinite series and applies the ideas to daily life. This unit leads into Grade 12 Mathematics Unit 2: Introduction to Calculus on Atenu.

Chapter 1.1 – Sequences

• First, a sequence as an ordered list of terms, with its general term aₙ.
• Then a recurrence relation that defines each term from earlier ones.

Chapter 1.2 – Arithmetic and Geometric Sequences

• First, an arithmetic sequence with a common difference d.
• Then a geometric sequence with a common ratio r.
• Also the nth term of each, aₙ = a₁ + (n − 1)d and aₙ = a₁rⁿ⁻¹.

Chapter 1.3 – The Sigma Notation and Partial Sums

• First, writing a sum compactly with the sigma notation Σ.
• Then the partial sum of an arithmetic series, Sₙ = n(a₁ + aₙ)/2.
• Also the partial sum of a geometric series.

Chapter 1.4 – Infinite Series

• First, the sum of an infinite geometric series when |r| < 1.
• Then the idea of convergence and divergence.

Chapter 1.5 – Applications

• Finally, using sequences and series in savings, loans, and growth problems.

Learning Outcomes

• Find the general term of a sequence.
• Identify arithmetic and geometric sequences and their terms.
• Use sigma notation to write a sum.
• Compute the partial sum of an arithmetic or geometric series.
• Find the sum of a convergent infinite geometric series.
• Finally, apply sequences and series to real-life problems.