Sequences and Series Pg. 1
Sequences and Series Exercise Find the first four terms of the sequence 3 1, 1, 2, 3, . [Answer: 2, 5, 8, 11] Example Let be the sequence defined by 2, 1, and 21 13 2 for 0,1,2,, find and . Solution: (k = 0) 21 13 2 2 2 3 (k = 1) 32 24 2 6 2 8 ⁄ Exercise Without using a calculator, find the first 4 terms of the recursively defined sequence • 5, 2 3 [Answer: 5, 7, 11, 19] • 4, 1 [Answer: 4, , , ] • 2, 3, [Answer: 2, 3, 5, 8] Example Evaluate ∑ 0.5 and round your answer to 5 decimal places. ! Solution: ∑ 0.5 ! 0.5 0.5 0.5 ! ! ! 0.5 0.5 ! ! 0.5 0.5 0.5 0.5 0.5 0.5 0.041666 0.003125 0.000186 0.000009 . Exercise Find and evaluate each of the following sums • ∑ [Answer: 225] • ∑ 1 5 [Answer: 521] pg. 1 Sequences and Series Arithmetic Sequences an = an‐1 + d, also an = a1 + (n – 1)d n S = ()a +a n 2 1 n Exercise • For the arithmetic sequence 4, 7, 10, 13, (a) find the 2011th term; [Answer: 6,034] (b) which term is 295? [Answer: 98th term] (c) find the sum of the first 750 terms. [Answer: 845,625] rd th • The 3 term of an arithmetic sequence is 8 and the 16 term is 47. Find and d and construct the sequence. [Answer: 2,3;the sequence is 2,5,8,11,] • Find the sum of the first 800 natural numbers. [Answer: 320,400] • Find the sum ∑ 4 5.
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