Worksheet 1: Patterns, Sequences and Series Grade 12 ...

1 Worksheet 1: Patterns, Sequences and Series Grade 12 Mathematics CAPS 1. For each pattern: i) Determine whether the pattern is arithmetic, quadratic or geometric . ii) Find the general term Tn in terms of n iii) And find the 11th term a) 8; 4; 2; 1; .. b) ; 5; ; 13; .. c) 8; 10; 12; 14; .. d) 1; 3; 9; 27; .. e) ; ; ; ; .. f) 3; 12; 48; 192; .. g) 6; 10; 16; 24; .. h) 2; 6; 10; 14; .. i) 4; 11; 18; 25; .. j) ; ; ; ; .. 2. Give the first five terms for the general terms given below: a) b) ( ) c) d) ( ) e) ( ) 3. Calculate: a) b) c) d) ( ) e) ( ) 4. Derive the formula for: a) [ ( ) ] b) ( ) 5. Find the sum for each of these Series : a) 40 + 20 + 10 + .. + b) 83 + 79 + 75 +.

2 + 23 c) 48 + 57 + 66+ .. + 93 d) 1 + 5 + 25 + .. + 244 140 625 e) 28 + 14 + 7+ .. + 6. Say whether each of these Series are diverging or converging: a) 28 + 14 + 7 + .. b) 45 + 15 + 5 + .. c) 6 + 12 + 24 + .. d) 66 + + .. e) ( ) f) ( ) 7. For each of the Series that are converging in question 6, determine their sum to infinity. 8. An arithmetic and geometric Series both have the same first term, a = 9. The fifth term of the arithmetic Series is equal to the second term of the geometric Series minus 1. The sum of first three terms of the geometric Series is equal to the twenty-eighth term of the arithmetric Series . a) Find the ratio and common difference for each of the Series (if the common difference is a whole number) b) Is the geometric Series converging or diverging? If it is converging, determine the sum to infinity.

3 C) Find the sum of the first 15 numbers of the arithmetic Series . d) Will the sum of the first 5 geometric terms be equal to a term in the arithmetic Series ? If it is, what term is it? 9. The second term of a geometric Series is 2, and the sum to infinity of the geometric Series is 9. a) Find the first term and the common ratio. b) Find the 10th term of the Series . c) Find the sum of the first 10 terms. 10. The sum of the first 5 terms of an arithmetic Series is 3. The fifth term is of the Series is . a) Determine the first term and the common difference. b) Which term will be equal to 0? c) When will the sum of the arithmetic Series be equal to 0? 11. If ( ) Determine the value of n. 12. For which values of will 13. The eleventh term of an arithmetic Series is 45 and the 8th term in the arithmetic Series is 33. Find the 15th term of the Series and the sum of the first 20 terms of the Series .

4 14. A geometric Series has a fourth term equal to 128 and a seventh term equal to . Find the sum to infinity of the Series . 15. The first 10 terms of an arithmetic Series sum to 465 while the sum of the first 20 terms have a sum of 430. a) Find the first term and the common difference. b) Which term is equal to -1? c) For what value of n would the sum of the Series be less than 0? 16. Given the following Series : 5 6 12 12 19 24 26 48 a) Give the next 4 terms of the Series . b) Find the sum of the first 50 terms. c) What will the 45th term be?