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1 ) Find the general term u n for an arithmetic sequence given that u 3 = 8 and u 8 = -17

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad , Glen Whiffen , John Owen, Robert Haese , Sandra Haese and Mark Bruce Haese and Haese Publications, 2004. Section 12CG – Arithmetic Sequences and Series.

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1 ) Find the general term u n for an arithmetic sequence given that u 3 = 8 and u 8 = -17

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  1. Material Taken From:Mathematicsfor the international student Mathematical Studies SLMal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark BruceHaese and Haese Publications, 2004

  2. Section 12CG – Arithmetic Sequences and Series 1) Find the general term un for an arithmetic sequence given that u3 = 8 and u8 = -17

  3. 2) Insert four numbers between 3 and 12 so that all six numbers are in arithmetic sequence.

  4. The sum of the n terms of an arithmetic series OR

  5. 3) Find the sum of 4 + 7 + 10 + 13 + … to 50 terms.

  6. 4) Find the sum of -6 + 1 + 8 + 15 + … + 141

  7. 5) The first five terms of an arithmetic sequence are shown below.2, 6, 10, 14, 18(a) Write down the sixth number in the sequence.(b) Calculate the 200th term.(c) Calculate the sum of the first 90 terms of the sequence.

  8. Section 12DG – Geometric Sequences and Series A geometric sequence: • occurs when each term can be obtained from the previous one by multiplying by the same non-zero constant. • 4, 12, 36, 108, … • 125, 25, 5, 1, … Algebraic Definition: {un} is geometric if (and only if) un + 1 = r un for all positive integers n where r is a constant (the common ratio)

  9. The General Term of a geometric sequence

  10. 1) For the sequence Show that the sequence is geometric Find the general term un. Hence, find the 12th term as a fraction.

  11. 2) k – 1, 2k and 21 – k are consecutive terms of a geometric sequence. Find k.

  12. 3) A geometric sequence has u2 = -6 and u5 = 162. Find its general term.

  13. 4) Find the first term of the geometric sequence which exceeds 1400.

  14. Homework • Pg 404 – Section 12C • #8 • Pg 406-407 – Section 12D • #3, 4, 6bc, 7bd, 8b

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