2.1

Topic

Change in Arithmetic and Geometric Sequences

Practice by unit: Exponential and Logarithmic Functions

Sub-standards

• 2.1.A.1 — Express arithmetic sequences found in mathematical and contextual scenarios as functions of the whole numbers. A sequence is a function from the whole numbers to the real numbers. Consequently, the graph of a sequence consists of discrete points instead of a curve.
• 2.1.A.2 — Successive terms in an arithmetic sequence have a common difference, or constant rate of change.
• 2.1.A.3 — The general term of an arithmetic sequence with a common difference d is denoted by an and is given by an = a d 0 + n, where a0 is the initial value, or by an = a + d(n k − ) k , where ak is the kth term of the sequence.
• 2.1.B.1 — Express geometric sequences found in mathematical and contextual scenarios as functions of the whole numbers. Successive terms in a geometric sequence have a common ratio, or constant proportional change.
• 2.1.B.2 — The general term of a geometric sequence with a common ratio r is denoted by gn and is given n gn = g r by 0 , where g0 is the initial value, or by (n k − ) g = g r n k , where gk is the kth term of the sequence.
• 2.1.B.3 — Increasing arithmetic sequences increase equally with each step, whereas increasing geometric sequences increase by a larger amount with each successive step. UNIT 2