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 ““, “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 = t₁ + d(n – 1).

Example: Find t₁₀: 0, 1, 2, 3, 4

= ? = 0 d = +1 n = 10

= 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.