How can a sequence be defined explicitly?
By a formula like .
What is the first step to calculate terms of a recursive sequence?
Start from the given initial term(s).
What defines an arithmetic sequence?
Adding the same number called common difference to each term gives the next term.
What is the explicit formula for an arithmetic sequence with first term and difference ?
for every natural number .
Sequence notation label
Explicit or recursive definition
Arithmetic sequence formula
Arithmetic sum formula
n(n+1)/2 for sum 1 to n
Geometric sequence ratio
Same number q multiplies previous term
Arithmetic sequence explicit form
u_0 + r * n
Recurrence model
Connects current and previous terms
Sum of powers of q
Sum from i=0 to n of q^i
Answer 9 questions on Sequences and Recurrence Relations.
1. Which statement correctly distinguishes an explicit definition from a recursive definition of a sequence?
2. A sequence is defined by and . What is ?
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