IB Math Studies Yr 1 Sequences and Series Review, Schemes and Mind Maps of Calculus

Download IB Math Studies Yr 1 Sequences and Series Review and more Schemes and Mind Maps Calculus in PDF only on Docsity! IB Math Studies Yr 1 Name_________________________________ Date_______________ 6-13 Test Review #2 Unit 6 Sequences and Series Test Review #2 Directions: Complete each question to the best of your ability. You may use your notes. Be sure to clearly mark your answers and work. Unless otherwise stated leave all answers as exact or rounded to 3 significant figures. To receive full credit, you must complete the following:  Show all of your work  Check your work using the answer key. Show evidence of checking your work (correct any mistakes IN A DIFFERENT COLOR) Arithmetic and Geometric Cheat Sheet ARITHMETIC GEOMETRIC DEFINITION add to get next term (common difference) multiply to get next term (common ratio) KEY WORDS “arithmetic”, “common difference” “geometric”, “common ratio” SEQUENCE FORMULA (rule) 𝑢𝑛 = 𝑢1 + (𝑛 − 1)𝑑 𝑢𝑛 = 𝑢1 ∙ 𝑟 𝑛−1 SERIES FORMULA (rule) 𝑆𝑛 = 𝑛 2 [2𝑢1 + (𝑛 − 1)𝑑] 𝑆𝑛 = 𝑢1(1 − 𝑟𝑛) 1 − 𝑟 FINDING THE PATTERN 𝑑 = 𝑢2 − 𝑢1 or 𝑑 = 𝑦2 − 𝑦1 𝑥2 − 𝑥1 𝑟 = 𝑢2 𝑢1 WORD PROBLEMS “increasing by a constant” “decreasing by a constant” “increasing by a percent” “decreasing by a percent” “doubles”, “triples”, “halves”, etc..  Before you begin to answer the questions, be sure to identify if the sequence is arithmetic or geometric.  Look for keywords in the question that can inform you if it is arithmetic or geometric.  Write out the sequence and determine if you are adding or multiplying to get to your next term.  Identify what the variable n represents in the context of the question. (nth row, nth day, nth year, etc…)  Carefully read the question to see if they are asking you to find n or 𝒖𝒏. Use the context of the question!  Determine if the given question requires the use of the sequence or series formulas. IB Math Studies Yr 1 IB TEST QUESTIONS 1. The first three terms of a geometric sequence are u1 = 512, u2 = 128, u3 = 32 (a) Find the value of r, the common ratio of the sequence. (b) Find the value of n for which un = 2 (c) Find the sum of the first 25 terms of the sequence. 2. The sixth term of an arithmetic sequence is 24. The common difference is 8. (a) Calculate the first term of the sequence. (b) Calculate the sum of the first 15 terms of the sequence.