In this chapter, we will be learning about progressions.
Progressions are sequences of numbers that follow a specific pattern.
We will start by studying arithmetic progressions, which are sequences where the difference between consecutive terms is constant.
We will learn how to identify arithmetic progressions and derive the formula for finding the nth term.
We will also practice using this formula in different situations.
Next, we will move on to geometric progressions, which are sequences where the ratio between consecutive terms is constant.
We will learn how to identify geometric progressions and use the formula for finding the nth term.
• Identify a sequence as an arithmetic progression and provide justification
• Derive the formula of the nth term, T_n, of arithmetic progressions, and hence use the formula in various situations
• Derive the formula of sum of the first n terms, S_n, of arithmetic progressions, and hence use the formula in various situations
• Solve problems involving arithmetic progressions
• Identify a sequence as a geometric progression and provide justification
• Derive the formula of the nth term, T_n, of geometric progressions, and hence use the formula in various situations
• Derive the formula of sum of the first n terms, S_n, of geometric progressions, and hence use the formula in various situations
• Determine the sum to infinity of geometric progressions, S_inf and hence use the formula in various situations
• Solve problems involving geometric progressions
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