12.2 & 12.5 – Arithmetic Sequences Arithmetic : Pattern is ADD or SUBTRACT same number each time. d = common difference – If add: d positive – If subtract:

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Presentation transcript:

12.2 & 12.5 – Arithmetic Sequences Arithmetic : Pattern is ADD or SUBTRACT same number each time. d = common difference – If add: d positive – If subtract: d negative Explicit Formula a = a₁ + (n-1)(d) – Must know FIRST TERM & DIFFERENCE – SIMPLIFY Distribute Combine like terms

Examples 1. Are these sequences ARITHMETIC? If yes, what is the d? A) 1,-2,-5,-8,-11,… B) 3,6,12,24,… C) 5,7,9,11,13,…

Examples: 2. Write a rule (explicit formula) for the arithmetic sequence. Then find a₂₀. A) 5,11,17,23,29,… B) 20,15,10,5,…

Explicit formula if unknown info If either (or both) the FIRST TERM & the DIFFERENCE are unknown, then a variation of the explicit formula is used. (once for each unknown – then traditional formula is used) Later = sooner + (subtract subscripts)(d) – Find d – Use found d, unknown first term & a given term to find a₁ – Use found d and found a₁ in traditional explicit formula and simplify.

Example: 3. Write the rule (explicit formula) for the nth term, then graph first 6 terms. a₄=96, d=-14

Example Write the rule (explicit) for the nth term. a₆=39 and a₁₄=79

Recursive Formula 2 Parts: a₁ = # and a = a + # Ex: Write recursive formula(rule):1,-2,-5,-8,-11 Ex: Write recursive formula(rule):7,9,11,13 Ex: Write the first 5 terms: a₁=5, a = a +4

Arithmetic Sum (SERIES) To find the SUM of a finite number or terms S = (n/2) (starting value + ending value) Find the SUM of the arithmetic series (-9+11n) Find the SUM of the arithmetic series (-3n +10)