Pre U TOPIC REVIEW
Term 1asequences and arithmetic series
1. Write down all of the terms of the following series:
a) / / b) / / c) / / (3 marks)2. Express the following using sigma notation:
a) / 12 + 22 + 32 + 42 / b) /c) / / (3 marks)
3. a) Write down the first 5 terms of the following sequences.
(i) / / (ii) / / (4 marks)b) For sequence (ii), write down the value of , giving a reason for your answer. (2 marks)
4. An arithmetic series has a first term of 3 and a common difference of 2.
a) Write down the first four terms of the series and the nth term. (2 marks)
b) Calculate the sum of the first 20 terms. (2 marks)
c) Determine the number of terms needed for the sum to exceed 1000. (4 marks)
5. Evaluate these series.
a) / / b) / 25 + 29 + 33 + ………… + 409 / (6 marks)6. Find, giving your answer in the form , where a and b are integers.(4 marks)
7.A piece of string 10m long is cut into pieces so that the lengths form an arithmetic sequence. The longest piece is 1m and the shortest is 25cm. How many pieces are there? (3 marks)
8. Find the sum of all the integers between 1 and 200 that are not multiples of 7.(6 marks)
9. The sum of the first ten terms of an arithmetic series is 50, and the sum of the first twenty terms is 180. Find the first term and the common difference of the series. (6 marks)
10.A company offers two salary schemes, designed to give equal total pay over a five-year period.
Scheme A : £14000 for the first year, increasing by £3425 per year.
Scheme B : £1000 for the first month, increasing by £d per month.
Find the value of d.(5 marks)