Geometric sequences Problem set A Answers

1. (a) 1536
2. (b) 2916
3. (c) 0.3125

1. (a) \(r = 3,\ u_1 = 2\)
2. (b) \(r = 2,\ u_1 = 5\) or \(r = -2,\ u_1 = 5\)

1. (a) \(5 \times 3^{n-1}\)
2. (b) \(64 \times \left(\tfrac{1}{2}\right)^{n-1}\)

1. (a) 10
2. (b) The 7th term, 12 288

\(2 \times 0.7^5 = 0.336\) m

(a) \(42\,000 \times 1.025^8 \approx 51\,200\) (b) 15 years

£8 359.27 (about £8 360)

(a) £15 353.12 (b) 5 years

\((x+4)^2 = x(x+12)\) gives \(x = 4\); the terms are 4, 8, 16 and \(r = 2\).