Standard +0.8 This question requires setting up and solving an equation involving a recurrence relation and a summation constraint. Students must expand the first 5 terms using the recurrence relation, sum them, set equal to 12, and solve for k while checking the constraint that terms are different (k ≠ 1). It combines sequences, series, and algebraic manipulation in a non-routine way that goes beyond standard textbook exercises.
A sequence of terms \(a_1, a_2, a_3, ...\) is defined by
$$a_1 = 4$$
$$a_{n+1} = ka_n + 3$$
where \(k\) is a constant.
Given that
• \(\sum_{n=1}^{5} a_n = 12\)
• all terms of the sequence are different
find the value of \(k\) [4]
A sequence of terms $a_1, a_2, a_3, ...$ is defined by
$$a_1 = 4$$
$$a_{n+1} = ka_n + 3$$
where $k$ is a constant.
Given that
• $\sum_{n=1}^{5} a_n = 12$
• all terms of the sequence are different
find the value of $k$ [4]
\hfill \mbox{\textit{SPS SPS FM 2025 Q8 [4]}}