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### Sequences and Series

Ex. 0:
A sequence has the following terms: u4 = 0.04, u5 = 0.01, u6 = 0.00, u7 = 0.00, u8 = 0.00, u9 = 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 = 17.00, r = 0.13, u15 = 0.00]
Ex. 1:
A geometric sequence has the following terms: u5 = 0.010, u6 = -0.002, 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 = 6.00, r = -0.20, Sinf = 5.00]
Ex. 2:
A geometric sequence has the following terms: u4 = -0.019, u5 = -0.002, u6 = -0.000, u7 = -0.000, 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 = -14.00, r = 0.11, Sinf = -15.75]
Ex. 3:
A sequence has the following terms: a6 = -38, a7 = -45, a8 = -52, a9 = -59, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 17th term (a17).
[Arithmetic, a1 = 4, d = -7, a17 = -108]
Ex. 4:
A sequence has the following terms: a8 = -114, a9 = -126, a10 = -138, a11 = -150, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 34th term (a34).
[Arithmetic, a1 = -18, d = -12, a34 = -414]
Ex. 5:
A geometric sequence has the following terms: u4 = 0.020, u5 = 0.003, u6 = 0.000, u7 = 0.000, 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 = 7.00, r = 0.14, Sinf = 8.17]
Ex. 6:
A sequence has the following terms: a6 = 62, a7 = 70, a8 = 78, a9 = 86, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 50th term (a50).
[Arithmetic, a1 = 14, d = 8, a50 = 406]
Ex. 7:
A sequence has the following terms: a6 = 25, a7 = 27, a8 = 29, a9 = 31, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 33th term (a33).
[Arithmetic, a1 = 13, d = 2, a33 = 77]
Ex. 8:
A sequence has the following terms: u4 = 4.44, u5 = 2.96, u6 = 1.98, u7 = 1.32, u8 = 0.88, u9 = 0.59, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 14th term (a14).
[Geometric, u1 = 15.00, r = 0.67, u14 = 0.08]
Ex. 9:
A sequence has the following terms: u3 = 0.52, u4 = 0.10, u5 = 0.02, u6 = 0.00, u7 = 0.00, u8 = 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 = 13.00, r = 0.20, u15 = 0.00]

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