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## Jeopardy

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**Jeopardy**Choose a category. You will be given a question. You must give the correct answer. Click to begin.**Choose a point value.**Choose a point value. Click here for Final Jeopardy**Sequences**Arithmetic Sequences Geometric Sequences Mathematical Induction Finite Differences 10 Point 10 Point 10 Point 10 Point 10 Point 20 Points 20 Points 20 Points 20 Points 20 Points 30 Points 30 Points 30 Points 30 Points 30 Points 40 Points 40 Points 40 Points 40 Points 40 Points 50 Points 50 Points 50 Points 50 Points 50 Points**Find the 5th term if**• an = 2n2 – n!**Find the 5th term if**• an = 2n2 – n! • 2(25) – 5(4)(3)(2)(1) = • – 70**Find the 5th term**• of this sequence: • a1 = 2; a2 = 5; • an = an-1 +an-2**Find the 5th term**• of this sequence: • a1 = 2; a2 = 5; • an = an-1 +an-2 • a1 = 2, a2 = 5, a3 = 7, • a4 = 12, a5 = 19**A sequence is an ordered list of numbers; a series is a sum.****Find the first term without a calculator:**an = n / (n – 1)!**Find the first term:**an = n/(n – 1)! a1= 1/0! = 1/1 = 1**The terms in an arithmetic sequence have a common**difference.**What is the formula for the explicit formula for an**arithmetic sequence?**Find the 101st term:**1 + 3 + 5 + …**1 + 3 + 5 + …**a101 = a1+(n – 1)(d) a101 = 1+100(2) = 201**Write in sigma notation:**1 + 4 + 7 + …+ 31**Write the recursive formula if a5 = 6 and a10 = 16.**a1 = –2; an = an – 1+ 2**What is the recursive formula for a geometric sequence?**a1 = ___; an = ran – 1**Find the explicit formula:**½, –1, 2, – 4, …**Find the explicit formula:**½, –1, 2, – 4, … an = ½ (–2) n – 1 or (–1) n – 1(2) n – 2**Find the sum:**.25 + .0025 + .000025 + …**.25 + .0025 + .000025 + …=**a1/(1 – r) = .25/(1 – .01) = .25/.99 = 25/99**Assume that the equation is true for**n = some natural number k.**Show that if the equation is true for**n = k, then it is also true for n = k + 1.**Mathematical induction allows you to prove that an equation**is true for all natural numbers.**What would you add to the left hand side to show that this**equation is true by mathematical induction? 1 + 4 + …+ k2 = k(k – 1 )/2**1 + 4 + …+ k2+ (k + 1) 2**= k(k – 1 )/2**How do you know the degree of an equation based on finite**differences?**The degree of the equation is how many levels of differences**you need for them to repeat.**The leading coefficient is the value of the difference that**repeats divided by the degree factorial.**Find the first term of an equation for this sequence:**3, 6, 13, 24, 39, …**3, 6, 13, 24, 39, …**3 7 11 15 4 4 4 degree = 2, l.c. = 4/2! = 2 2x2**Given this sequence, 3, 6, 13, 24, 39, …and y = 2x2, find**its next term.