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### Sequences and Series

Ex. 0:
A geometric sequence has the following terms: u3 = -0.327, u4 = 0.047, u5 = -0.007, u6 = 0.001, 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 = -16.00, r = -0.14, Sinf = -14.00]
Ex. 1:
A sequence has the following terms: u4 = -0.64, u5 = 0.23, u6 = -0.09, u7 = 0.03, u8 = -0.01, u9 = 0.00, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 16th term (a16).
[Geometric, u1 = 13.00, r = -0.37, u16 = -0.00]
Ex. 2:
A sequence has the following terms: u4 = -12.65, u5 = 12.22, u6 = -11.82, u7 = 11.42, u8 = -11.04, u9 = 10.67, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 15th term (a15).
[Geometric, u1 = 14.00, r = -0.97, u15 = 8.71]
Ex. 3:
A geometric sequence has the following terms: u5 = 0.070, u6 = -0.018, u7 = 0.004, 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 = 18.00, r = -0.25, Sinf = 14.40]
Ex. 4:
A sequence has the following terms: u5 = -0.10, u6 = -0.03, 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 = -19.00, r = 0.27, u17 = -0.00]
Ex. 5:
A geometric sequence has the following terms: u3 = -2.250, u4 = -1.125, u5 = -0.563, u6 = -0.281, u7 = -0.141, u8 = -0.070, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = -9.00, r = 0.50, Sinf = -18.00]
Ex. 6:
A sequence has the following terms: a5 = 80, a6 = 95, a7 = 110, a8 = 125, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 34th term (a34).
[Arithmetic, a1 = 5, d = 15, a34 = 500]
Ex. 7:
A sequence has the following terms: a6 = -17, a7 = -21, a8 = -25, a9 = -29, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 41th term (a41).
[Arithmetic, a1 = 7, d = -4, a41 = -153]
Ex. 8:
A sequence has the following terms: u4 = -7.16, u5 = -6.21, u6 = -5.38, u7 = -4.66, u8 = -4.04, u9 = -3.50, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 14th term (a14).
[Geometric, u1 = -11.00, r = 0.87, u14 = -1.71]
Ex. 9:
A sequence has the following terms: a7 = -10, a8 = -10, a9 = -10, a10 = -10, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 46th term (a46).
[Arithmetic, a1 = -10, d = 0, a46 = -10]