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Proper, Improper and Mixed Fractions
Fractional Arithmetic
Changing the Subject of an Expression
Multiplying Expressions
Factorising Quadratic Expressions
Solving Linear Equations
Rationalising the Denominator
Solving Simultaneous (Linear) Equations
Solving Simultaneous Quadratic Equations
2 and 3 Part Ratios
Completing the Square
Sequences and Series
Ex. 0:
A sequence has the following terms: u5 = -1.54, u6 = -0.82, u7 = -0.44, u8 = -0.23, u9 = -0.12, u10 = -0.07, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 16th term (a16).
[Geometric, u1 = -19.00, r = 0.53, u16 = -0.00]
Ex. 1:
A sequence has the following terms: a7 = 6, a8 = 5, a9 = 4, a10 = 3, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 46th term (a46).
[Arithmetic, a1 = 13, d = -1, a46 = -32]
Ex. 2:
A sequence has the following terms: u3 = 11.11, u4 = 9.26, u5 = 7.72, u6 = 6.43, u7 = 5.36, u8 = 4.47, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 13th term (a13).
[Geometric, u1 = 16.00, r = 0.83, u13 = 1.79]
Ex. 3:
A geometric sequence has the following terms: u3 = 0.234, u4 = 0.029, u5 = 0.004, u6 = 0.000, u7 = 0.000, u8 = 0.000, ...Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = 15.00, r = 0.13, Sinf = 17.14]
Ex. 4:
A sequence has the following terms: u5 = -0.07, u6 = -0.02, u7 = -0.01, u8 = -0.00, u9 = -0.00, u10 = -0.00, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 17th term (a17).
[Geometric, u1 = -6.00, r = 0.33, u17 = -0.00]
Ex. 5:
A sequence has the following terms: a8 = -64, a9 = -72, a10 = -80, a11 = -88, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 27th term (a27).
[Arithmetic, a1 = 0, d = -8, a27 = -208]
Ex. 6:
A sequence has the following terms: a3 = -3, a4 = 1, a5 = 5, a6 = 9, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 56th term (a56).
[Arithmetic, a1 = -15, d = 4, a56 = 205]
Ex. 7:
A sequence has the following terms: u3 = 0.56, u4 = 0.24, u5 = 0.11, u6 = 0.05, u7 = 0.02, u8 = 0.01, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 15th term (a15).
[Geometric, u1 = 3.00, r = 0.43, u15 = 0.00]
Ex. 8:
A geometric sequence has the following terms: u5 = 0.055, u6 = -0.014, u7 = 0.003, u8 = -0.001, u9 = 0.000, u10 = -0.000, ...Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = 14.00, r = -0.25, Sinf = 11.20]
Ex. 9:
A sequence has the following terms: a9 = -112, a10 = -125, a11 = -138, a12 = -151, ...What type of sequence is it? Find the first term and the common difference/ratio, and hence the 33th term (a33).
[Arithmetic, a1 = 5, d = -13, a33 = -411]