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 the common ratio of the series.
Show that the n n\,nth term of the series, unu_nun, can be written as un=2n+13n−3u_n = \dfrac{2^{n+1}}{3^{n-3}}un=3n−32n+1.
Hence show that log3un=n(log32−1)+log32+3\log_3 u_n = n\left(\log_3 2 - 1\right) + \log_3 2 + 3log3un=n(log32−1)+log32+3.
231 exam-style questions on WJEC A Level Maths 3.4 Sequences and Series (A-level only), covering 3.4.1 Sequences and Series (A-level only), 3.4.2 Sequences and Series (A-level only), 3.4.3 Sequences and Series (A-level only), 3.4.4 Sequences and Series (A-level only), 3.4.5 Sequences and Series (A-level only), 3.4.6 Sequences and Series (A-level only), and 3.4.7 Sequences and Series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.