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1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following: a) what is d, the difference between any two consecutive terms? Answer: The common difference, d, can be found by subtracting the first term from the second term add 2 to each term to arrive at the next term, or...the difference a2 - a1 is 2. So d=2 b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: To find any term of an arithmetic sequence: where a1 is the first term of the sequence , d is the common difference, n is the number of the term to find. n = 101; a1 =2, d = 2 a101=2+(101-1)2 a 101 = 2+(100)2 =202 So the 101st term is 202 c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms? Answer: The common difference d for the sequence is 2. The first term a is 2. The number of terms is 20. Substituting a = 2, d = 2, n = 20 in the formula for the sum of n terms Sn 20 (2 * 2 (20 1)2) 420 2 Sn =420 d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms? Answer: a=2,d=2 and n=30 S n 30 (2(2) (30 1)2 930 2 Sn =930 e) What observation can you make about the successive partial sums of this sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Answer: 2+4 = 6 4+6 =10 6+8 =14 8+10=18 Every sum is larger than the previous and the difference between sums is growing by4 2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: The common ratio, r, can be found by dividing the second term by the first term Here second term=3 and first term =1 so r= 3 3 1 The ratio r=3