Patterns, sequences, and series

Practice 5 items →

Sequences are functions on the positive integers. Students write explicit and recursive forms for arithmetic and geometric sequences, find any term from two given terms, and sum a short arithmetic series.

Specification · for a parent or teacher

Part no.: arithmetic-geometric-sequences
Course: High School Math 1 · Unit 13
Realm: Change
Difficulty: 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

classify arithmetic vs geometric; write explicit and recursive forms; find any term from two given terms; write a sequence as a function on $\mathbb{Z}^+$ ; sum a short arithmetic series.

Ready when

12th term of an arithmetic and of a geometric sequence, from two given terms.

Formulas

Arithmetic

a_n = a_1 + (n-1)d

Geometric

g_n = g_1 r^{n-1}

Sum of first n integers

\sum_{i=1}^{n} i = \frac{n(n+1)}{2}

Watch for

$a_n=a_1+nd$ ; geometric with $r<0$ skipped.

Before · requires

Number patternssequences-patterns-7 · Math 7
Relations and functionsfunction-foundations · Math 1

After · used by

— none

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