C1 June 2011 Q5

EdexcelOld spec7 marksSequences & Series

5. A sequence \(a_1, a_2, a_3, \ldots\) is defined by\[\begin{aligned}a_1 &= k,\\ a_{n+1} &= 5a_n + 3, \qquad n \geqslant 1,\end{aligned}\]where \(k\) is a positive integer.

(a) Write down an expression for \(a_2\) in terms of \(k\). (1)
(b) Show that \(a_3 = 25k + 18\). (2)
(c)
(i) Find \(\displaystyle\sum_{r=1}^{4} a_r\) in terms of \(k\), in its simplest form.
(ii) Show that \(\displaystyle\sum_{r=1}^{4} a_r\) is divisible by 6.
(4)
‹ Previous59 of 159 in Sequences & SeriesNext ›