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  2. AP Pre Calculus
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Arithmetic sequence: Formula for the nth term (given initial term).

an=a0+dna_n = a_0 + dnan​=a0​+dn

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Arithmetic sequence: Formula for the nth term (given initial term).

an=a0+dna_n = a_0 + dnan​=a0​+dn

Arithmetic sequence: Formula for the nth term (given a known term).

an=ak+d(n−k)a_n = a_k + d(n-k)an​=ak​+d(n−k)

Geometric sequence: Formula for the nth term (given initial term).

gn=g0∗rng_n = g_0 * r^ngn​=g0​∗rn

Geometric sequence: Formula for the nth term (given a known term).

gn=gk∗r(n−k)g_n = g_k * r^(n-k)gn​=gk​∗r(n−k)

Arithmetic vs. Geometric: What is the key difference in how terms change?

Arithmetic: Constant addition/subtraction (common difference) | Geometric: Constant multiplication/division (common ratio)

Compare the growth patterns of arithmetic and geometric sequences.

Arithmetic: Linear growth | Geometric: Exponential growth

What characterizes the rate of change in an arithmetic sequence?

Constant rate of change, equal to the common difference.

What characterizes the rate of change in a geometric sequence?

Constant proportional change, equal to the common ratio.

Describe the graph of a sequence.

A set of discrete points, not a continuous curve, as the input is whole numbers.

How does an arithmetic sequence relate to linear growth?

Arithmetic sequences exhibit linear growth due to the constant addition of the common difference.

How does a geometric sequence relate to exponential growth?

Geometric sequences exhibit exponential growth due to the constant multiplication by the common ratio.