Pre IB Arithmetic Progression [33 marks]
1a. [2 marks]
The first term of an arithmetic sequence is 3 and the seventh term is 33.
Calculate the common difference;
1b. [2 marks]
Calculate the 95th term of the sequence;
1c. [2 marks]
Calculate the sum of the first 250 terms.
2a. [2 marks]
The first term, 𝑢1 , of an arithmetic sequence is 145. The fifth term, 𝑢5 , of the sequence is
113.
Find the common difference of the sequence.
2b. [2 marks]
The 𝑛th term, 𝑢𝑛 , of the sequence is 7.
Find the value of 𝑛.
2c. [2 marks]
The 𝑛th term, 𝑢𝑛 , of the sequence is 7.
Find 𝑆20 , the sum of the first twenty terms of the sequence.
3a. [2 marks]
The tenth term of an arithmetic sequence is 32 and the common difference is –6.
Find the first term of the sequence.
3b. [2 marks]
Find the 21st term of the sequence.
3c. [2 marks]
Find the sum of the first 30 terms of the sequence.
4a. [3 marks]
Maegan designs a decorative glass face for a new Fine Arts Centre. The glass face is made
up of small triangular panes. The first three levels of the glass face are illustrated in the
following diagram.
The 1st level, at the bottom of the glass face, has 5 triangular panes. The 2nd level has 7
triangular panes, and the 3rd level has 9 triangular panes. Each additional level has 2 more
triangular panes than the level below it.
Find the number of triangular panes in the 12th level.
4b. [3 marks]
Show that the total number of triangular panes, 𝑆𝑛 , in the first 𝑛 levels is given by:
𝑆𝑛 = 𝑛2 + 4𝑛.
4c. [2 marks]
Hence, find the total number of panes in a glass face with 18 levels.
4d. [3 marks]
Maegan has 1000 triangular panes to build the decorative glass face and does not want it to
have any incomplete levels.
Find the maximum number of complete levels that Maegan can build.
4e. [4 marks]
Each triangular pane has an area of 1.84m2 .
Find the total area of the decorative glass face, if the maximum number of complete levels
were built. Express your area to the nearest m2 .
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