Mathematics IB AA SL Sequences, Study notes of Mathematics

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Name__________________________________________________Date___________________________ Section 1.3 Worksheet

Name. Date. Section 1.3 Worksheet 1 For each finite series below, i decide whether the series is arithmetic or geometric ii find the sum of the series. a 174+19+21+...+u, b 36+28+20+...+U, © 54+10+20+...4+uU,, dd 76.34+75.54+ 74.7 +...4 Uy, e 64x +32x+16x+...+u, f (a+3)+(4a+12)+(16a+48)+...+u, 2. For each geometric series below, decide whether the series is converging or diverging. If the series is converging, find S,. a 1.6+2.44+3.64... b 81+544+36+... 4 5 c +i4+=4... d —4+14+—+... | 00 wih Nie 3 Find the sum of the first 24 terms of the series 50 + 44 + 38 + ... 4 Inan arithmetic sequence, the fifth term is two times the second term, and the sum of the first ten terms is 390. Find the first term and the common difference. 5 For the series 2+ 23 +6+63+..., find the least value of n for which S, >5000. 6 A geometric series has a first term of 2 and a common ratio of 3. Find the value of n if S, = 59048. 7 Aseries has the formula S, =2"-1. a Find the values of S;, S2, and S3. b Find the values of u:, u2, and us. ¢ Write a general formula for up. 8 For the series 90 + 60 + 40 + ..., find the value of r and the sum to infinity. 9 Consider the geometric sequence 2048, 1536, 1152, ... Find the least value of n such that the n‘” term of the sequence is less than 4. 10In a geometric sequence, the fourth term is 27 times the first term, and the sum of the first four terms is 68. Find the first term and the common ratio. 11 Consider a geometric series with S, = 490 and S, =625. Find the first term and the common ratio.