## Other tutor / coaching services: GCSE/A-level Computer Science

### Sequences and Series

Ex. 0:
A geometric sequence has the following terms: u5 = 0.001, 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 = 5.00, r = -0.13, Sinf = 4.44]
Ex. 1:
A sequence has the following terms: a7 = -125, a8 = -141, a9 = -157, a10 = -173, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 29th term (a29).
[Arithmetic, a1 = -13, d = -16, a29 = -461]
Ex. 2:
A sequence has the following terms: a7 = -83, a8 = -96, a9 = -109, a10 = -122, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 56th term (a56).
[Arithmetic, a1 = 8, d = -13, a56 = -707]
Ex. 3:
A sequence has the following terms: u3 = 0.02, u4 = -0.00, u5 = 0.00, 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 = 14.00, r = -0.03, u15 = 0.00]
Ex. 4:
A sequence has the following terms: u4 = -1.46, u5 = -0.63, u6 = -0.28, u7 = -0.12, u8 = -0.05, u9 = -0.02, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 13th term (a13).
[Geometric, u1 = -18.00, r = 0.43, u13 = -0.00]
Ex. 5:
A sequence has the following terms: u3 = 1.76, u4 = 0.70, u5 = 0.28, u6 = 0.11, u7 = 0.05, u8 = 0.02, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 15th term (a15).
[Geometric, u1 = 11.00, r = 0.40, u15 = 0.00]
Ex. 6:
A geometric sequence has the following terms: u4 = 0.088, u5 = 0.018, u6 = 0.004, 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 = 11.00, r = 0.20, Sinf = 13.75]
Ex. 7:
A sequence has the following terms: u4 = 3.09, u5 = 1.75, u6 = 0.99, u7 = 0.56, u8 = 0.32, u9 = 0.18, ...
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 = 0.57, u15 = 0.01]
Ex. 8:
A sequence has the following terms: u5 = -0.56, u6 = -0.28, u7 = -0.14, u8 = -0.07, u9 = -0.04, u10 = -0.02, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 16th term (a16).
[Geometric, u1 = -9.00, r = 0.50, u16 = -0.00]
Ex. 9:
A sequence has the following terms: u4 = 1.75, u5 = 0.88, u6 = 0.44, u7 = 0.22, u8 = 0.11, u9 = 0.05, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 16th term (a16).
[Geometric, u1 = 14.00, r = 0.50, u16 = 0.00]