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

### Sequences and Series

Ex. 0:
A sequence has the following terms: a3 = 32, a4 = 43, a5 = 54, a6 = 65, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 25th term (a25).
[Arithmetic, a1 = -1, d = 11, a25 = 263]
Ex. 1:
A geometric sequence has the following terms: u5 = 4.000, u6 = -4.000, u7 = 4.000, u8 = -4.000, u9 = 4.000, u10 = -4.000, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = 4.00, r = -1.00, Sinf = 2.00]
Ex. 2:
A sequence has the following terms: a6 = 6, a7 = 4, a8 = 2, a9 = 0, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 37th term (a37).
[Arithmetic, a1 = 18, d = -2, a37 = -54]
Ex. 3:
A sequence has the following terms: u5 = -2.09, u6 = -1.32, u7 = -0.84, u8 = -0.53, u9 = -0.34, u10 = -0.21, ...
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 = 0.63, u16 = -0.01]
Ex. 4:
A geometric sequence has the following terms: u3 = 0.889, u4 = 0.296, u5 = 0.099, u6 = 0.033, u7 = 0.011, u8 = 0.004, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = 8.00, r = 0.33, Sinf = 12.00]
Ex. 5:
A sequence has the following terms: u4 = 4.63, u5 = -3.86, u6 = 3.22, u7 = -2.68, u8 = 2.23, u9 = -1.86, ...
What type of sequence is it? Find the first term and the common difference/ratio, and hence the 15th term (a15).
[Geometric, u1 = -8.00, r = -0.83, u15 = -0.62]
Ex. 6:
A sequence has the following terms: u3 = 0.17, u4 = -0.03, 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 12th term (a12).
[Geometric, u1 = 6.00, r = -0.17, u12 = -0.00]
Ex. 7:
A geometric sequence has the following terms: u3 = -0.680, u4 = 0.136, u5 = -0.027, u6 = 0.005, u7 = -0.001, u8 = 0.000, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = -17.00, r = -0.20, Sinf = -14.17]
Ex. 8:
A sequence has the following terms: u3 = -0.32, u4 = -0.06, u5 = -0.01, 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 12th term (a12).
[Geometric, u1 = -8.00, r = 0.20, u12 = -0.00]
Ex. 9:
A geometric sequence has the following terms: u3 = -1.188, u4 = 0.297, u5 = -0.074, u6 = 0.019, u7 = -0.005, u8 = 0.001, ...
Find the first term and the common ratio, and hence the sum to infinity (Sinf) of the series.
[u1 = -19.00, r = -0.25, Sinf = -15.20]