The sum to infinity of a geometric series is 108. The first term of the series is less than 40. The second term of the series is 24.
Find the first term and common ratio of the series.
(i) Show that the n n\,nth term of the series, unu_nun, can be written as un=2n+13n−3\displaystyle u_n = \frac{2^{n+1}}{3^{n-3}}un=3n−32n+1. (ii) Hence show that log3un=n(log32−1)+log32+3\log_3 u_n = n(\log_3 2 - 1) + \log_3 2 + 3log3un=n(log32−1)+log32+3.
326 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.