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Sequences and Series

Ex. 0:
A geometric sequence has the following terms: u4 = -0.128, u5 = -0.026, u6 = -0.005, u7 = -0.001, u8 = -0.000, u9 = -0.000, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = -16.00, r = 0.20, Sinf = -20.00]
Ex. 1:
A sequence has the following terms: a9 = 109, a10 = 122, a11 = 135, a12 = 148, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 39th term (a39).
[Arithmetic, a1 = -8, d = 13, a39 = 486]
Ex. 2:
A geometric sequence has the following terms: u5 = -0.007, u6 = -0.001, u7 = -0.000, u8 = -0.000, 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 = -9.00, r = 0.17, Sinf = -10.80]
Ex. 3:
A sequence has the following terms: u5 = -0.00, u6 = -0.00, u7 = -0.00, 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 15th term (a15).
[Geometric, u1 = -7.00, r = 0.10, u15 = -0.00]
Ex. 4:
A sequence has the following terms: a3 = 38, a4 = 55, a5 = 72, a6 = 89, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 18th term (a18).
[Arithmetic, a1 = -13, d = 17, a18 = 276]
Ex. 5:
A sequence has the following terms: a7 = -30, a8 = -34, a9 = -38, a10 = -42, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 46th term (a46).
[Arithmetic, a1 = -2, d = -4, a46 = -182]
Ex. 6:
A sequence has the following terms: a10 = -11, a11 = -14, a12 = -17, a13 = -20, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 40th term (a40).
[Arithmetic, a1 = 19, d = -3, a40 = -98]
Ex. 7:
A geometric sequence has the following terms: u5 = 0.002, u6 = 0.000, u7 = 0.000, u8 = 0.000, 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 = 12.00, r = 0.11, Sinf = 13.50]
Ex. 8:
A sequence has the following terms: a4 = 7, a5 = 6, a6 = 5, a7 = 4, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 26th term (a26).
[Arithmetic, a1 = 11, d = -1, a26 = -14]
Ex. 9:
A geometric sequence has the following terms: u3 = 0.111, u4 = -0.012, u5 = 0.001, 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 = 9.00, r = -0.11, Sinf = 8.10]