Moderate -0.5 This is a straightforward recurrence relation question requiring iterative calculation of terms using the given formula and initial value. It involves basic arithmetic and substitution with no conceptual difficulty beyond understanding the notation, making it slightly easier than a typical A-level question which would require more problem-solving or multiple techniques.
Sets \(u_1 + u_2 + u_3 = 117\) to produce equation in just \(k\)
\(6k^2+9k-105=0 \Rightarrow k = \ldots\)
dM1
Solves a 3TQ by any valid method to find at least one value for \(k\)
\(k = \frac{7}{2}\)
A1
\(k = \frac{7}{2}\) ONLY
# Question 2:
## Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempts to substitute $u_2 = 6k+3$ in $u_3 (= ku_2 + 3)$ | M1 | Allow if "+3" missing once only; may be implied by correct answer; incorrect answer with no substitution is M0 |
| $u_3 = k(6k+3)+3$ | A1 | OR $u_3 = 6k^2+3k+3$ but isw after correct answer seen |
## Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Uses $\sum_{n=1}^{3} u_n = 117 \Rightarrow 6+6k+3+k(6k+3)+3=117$ | M1 | Sets $u_1 + u_2 + u_3 = 117$ to produce equation in just $k$ |
| $6k^2+9k-105=0 \Rightarrow k = \ldots$ | dM1 | Solves a 3TQ by any valid method to find at least one value for $k$ |
| $k = \frac{7}{2}$ | A1 | $k = \frac{7}{2}$ ONLY |
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