# Week 1 – Precalc 11

This week in Pre-Calculus 11, we started the Sequences and Series unit. We first learned about arithmetic sequences.

Arithmetic sequence: a list of terms in which a common difference is added to each term to equal the next term

Term: a number (represented by “$t_n$“, “n” being the terms place in the arithmetic sequence)

Common difference: a common number added to each term to equal the next term (represented by “d”)

Example: 0, 1, 2, 3, 4     d = +1

t₁  t₂  t₃  t₄  t₅

To find the value of a term in an arithmetic sequence, we use the formula $t_n$ = t₁ + d(n – 1).

Example: Find t₁₀: 0, 1, 2, 3, 4

$t_{10}$ = ?     $t_1$ = 0     d = +1     n = 10

$t_n$ = t₁ + d(n – 1)

(t₁₀) = (0) + (1)[(10) – 1]

(t₁₀) = 0 + 1 · 9

(t₁₀) = 0 + 9

(t₁₀) = 9

This method of finding the values of terms in an arithmetic sequence is faster than extending the list.