Section 12.2: Arithmetic Sequences

1. Specify what makes an arithmetic sequence ‘arithmetic.’
2. Identify from three or more terms of a sequence, whether the sequence is arithmetic, and if the sequence is arithmetic, identify the first term \(a\) and common difference \(d\).
3. Identify and use the ‘trick’ for determining the \(n\)-th partial sum of an arithmetic sequence by appropriately pairing up the terms in the arithmetic sequence.
4. Given a situation that can be modeled using an arithmetic sequence or the partial sum of an arithmetic sequence, identify the appropriate arithmetic sequence and / or its partial sum.

Section 12.3: Geometric Sequences

1. Specify what makes a geometric sequence ‘geometric.’
2. Identify from three or more terms of a sequence, whether the sequence is geometric, and if the sequence is geometric, identify the first term \(a\) and common ratio \(r\).
3. Identify and use the ‘trick’ for determining the \(n\)-th partial sum of a geometric sequence by appropriately pairing up the terms of the geometric sequence and the terms of the geometric sequence times \(r\).
4. Given a situation that can be modeled using a geometric sequence or the partial sum of geometric sequence, identify the appropriate geometric sequence and / or its partial sum.