Arithmetic and Geometric Sequences Flashcards

Question 1

What is a sequence?

Accepted Answer

An ordered list of numbers $(a_1,a_2,a_3,\dots)$ where $a_n$ denotes the $n$th term.

Question 2

Find the 20th term of the arithmetic sequence with $a_1=5$ and $d=3$.

Accepted Answer

$a_{20}=5+(20-1)\cdot3=62$.

Question 3

What is the difference between an explicit formula and a recursive formula for a sequence?

Accepted Answer

Explicit gives $a_n$ directly in terms of $n$ (and parameters like $a_1,d,r$). Recursive defines $a_n$ from previous term(s), e.g., $a_n=a_{n-1}+d$ or $a_n=r\,a_{n-1}$ with a starting value.

Arithmetic and Geometric Sequences Flashcards

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