of the geometric sequence 8‚ –16‚ 32 … if there are 15 terms? (1 point) = 8 [(-2)^15 -1] / [(-2)-1] = 87384 2. What is the sum of the geometric sequence 4‚ 12‚ 36 … if there are 9 terms? (1 point) = 4(3^9 - 1)/(3 - 1) = 39364 3. What is the sum of a 6-term geometric sequence if the first term is 11‚ the last term is –11‚264 and the common ratio is –4? (1 point) = -11 (1-(-4^n))/(1-(-4)) = 11(1-(-11264/11))/(1-(-4)) = 2255 4. What is the sum of an 8-term geometric sequence
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× 10–2. 6. In an arithmetic sequence‚ the first term is 5 and the fourth term is 40. Find the second term. 7. If loga 2 = x and loga 5 = y‚ find in terms of x and y‚ expressions for (a) log2 5; (b) loga 20. 8. Find the sum of the infinite geometric series 9. Find the coefficient of a5b7 in the expansion of (a + b)12. 10. The Acme insurance company sells two savings plans‚ Plan A and Plan B. For Plan A‚ an investor starts with an initial deposit of $1000 and increases this by $80 each
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CHAPTER 7 ARITHMETIC AND GEOMETRIC PROGRESSIONS 7.1 Arithmetic Progression (A.P) 7.1.1 Definition The nth term of an arithmetic progression is given by ‚ where a is the first term and d the common difference. The nth term is also known as the general term‚ as it is a function of n. 7.1.2 The General Term (common difference) Example 7-1 In the following arithmetic progressions a. 2‚ 5‚ 8‚ 11‚ ... b. 10‚ 8‚ 6‚ 4‚ ... Write (i) the first term‚ (ii) the common difference‚
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ionGeometric Progression‚ Series & Sums Introduction A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term‚ i.e.‚ where | r | common ratio | | a1 | first term | | a2 | second term | | a3 | third term | | an-1 | the term before the n th term | | an | the n th term |
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Arithmetic Progressions (AP) An arithmetic progression is a list of numbers where the difference between successive numbers is constant. The terms in an arithmetic progression are usually denoted as T1 ‚ T2 ‚ and T3 ‚ where T1 is the initial term in the progression‚ T2 is the second term‚ and so on. Thus‚ Tn is the nth term of the arithmetic progression. An example of an arithmetic progression is…. 2; 4; 6; 8; 10; 12; 14; Since the difference between successive terms is constant‚ we have…
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This work MAT 126 Week 1 Assignment - Geometric and Arithmetic Sequence shows "Survey of Mathematical Methods" and contains solutions on the following problems: First Problem: question 35 page 230 Second Problem: question 37 page 230 Mathematics - General Mathematics Week One Written Assignment Following completion of your readings‚ complete exercises 35 and 37 in the “Real World Applications” section on page 280 of Mathematics in Our World . For each exercise‚
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Geometric mean From Wikipedia‚ the free encyclopedia Jump to: navigation‚ search The geometric mean‚ in mathematics‚ is a type of mean or average‚ which indicates the central tendency or typical value of a set of numbers. It is similar to the arithmetic mean‚ which is what most people think of with the word "average‚" except that instead of adding the set of numbers and then dividing the sum by the count of numbers in the set‚ n‚ the numbers are multiplied and then the nth root of the resulting
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Solutions 1. Mixture Problems: 2. Value of the Original Fraction: 3. Value of Numerical Coefficient: 4. Geometric Series: 5. Simplify: 6. Mean Proportion: 7. Value of x to form a geometric progression: 8. Value of x: 9. Work Problem: 10. Value of the original number: 11. Sum of the roots: A = 5‚ B = -10‚ C = 2 12. Work Problem: 13. Value of m: 14. Age Problem: Subject Past
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2013 JC1 December Holiday Assignment JJC 2012 H2 Mathematics Promotional Examination 1 −2 Expand ( k + y ) up to and including the term in y 2 ‚ where k is a non-zero constant. State the range of values of y for which the expansion is valid. [4] In the expansion of ( k + x + 2 x 2 ) −2 in ascending powers of x‚ the coefficient of x 2 is zero. Find the value of k. 2 The curve C has equation y = [3] 2x + a ‚ where a is a positive constant. By rewriting the equation x−3 B ‚ where A and B are
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edge. I.e – Each straight line - Becomes this - Hence now for everyone 1 line‚ 4 new ones are formed. Hence we can say that there is geometric progression‚ by the factor 4. Hence‚ the formula for the number of sides is Nn = 3(4)n Length of Side The length of the next side is one-third the previous length. This is once again geometric progression. Therefore‚ the equation for the nthterm is: Ln = Perimeter The perimeter of any shape = Length of each side x Number of sides Considering
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