Maths Worksheet - Geometric Series

SAEP Matric Success – Zisukhanyo Maths Worksheet Tuesday 17th March 2009 Number patterns – Geometric series 1. The fourth term of a geometric progression is 64 more than the third term. The sum of the third and fourth terms is 144. Determine the common ratio. 2. 1 + 2 + 4 + … is a geometric progression. a) What is the (n + 1)th term? b) Find the sum to n terms c) Prove that the sum to n terms is one less than the (n + 1)th term. 3. The second term of a geometric series is 6 and the fourth term is 54. Find the sums of the two possible series to 20 terms. 4. If the sum of the first four terms of a geometric series is 10 and the common ratio is 1/3, calculate the first term. 5. The first term of a geometric series is 27, the last term is 8 and the sum of the series is 65. What is the common ratio and how many terms are there in the series? 6. Find the sum of each of the following infinite geometric series. a) 7 + 7/5 + 7/25 + … b) 90 – 9 + 0,9 – 0,09 + … c) 5x + 5x/4 + 5x/16 + … d) 18 – 3 + ½ - 1/12 + … ∞

e)

∑3

1−n

f)

n =1 ∞

 2 g) ∑9 −  3 r =0 

n −1

∞

1    ∑ n =1  5 

∞

r

h)

∑2

−2 k

k =0

7. The sum to infinity of a GP is 10. The first term is 2. What is the constant ratio? 8. The n-th term of a series is given by 4(0,2)k – 1. a) Write down the first three terms of the series. b) Write down an expression for the sum of n terms of the series, without simplifying it. c) Determine the sum to infinity of the series 9. An acorn grows into a tree with a height of 2 m in its first year. Its growth each year thereafter is ¾ of its growth in the previous year. What is the greatest height it can reach?