| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | June |
| Marks | 3 |
| Topic | Arithmetic Sequences and Series |
| Type | Sequence defined by formula |
| Difficulty | Easy -1.3 This is a straightforward arithmetic sequence question requiring only direct substitution into a given formula, solving a simple linear equation, and applying the standard sum formula. All three parts are routine calculations with no problem-solving or conceptual challenge beyond basic recall of arithmetic series formulas. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
**(i)**
Obtain 8, 11, 14 **B1**
**[1]**
**(ii)**
Use correct formula $a + (n-1)d = 254$ **M1**
Obtain 83 **A1**
**[2]**
**(iii)**
Use correct sum formula for AP **M1**
Obtain $\frac{500}{2}(2(8) + (500-1)3)$ **A1**
Obtain 378 250 cao **A1**
*Alternative method:*
Obtain $8 + 499(3) = 1505$ and use correct $\frac{n}{2}(a + l)$ **M1**
Obtain $\frac{500}{2}(8 + 1505)$ **A1**
Obtain 378 250 cao **A1**
**[3]**4 A sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$, is defined by $u _ { n } = 3 n + 5$.\\
(i) State the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$.\\
(ii) Find the value of $n$ such that $u _ { n } = 254$.\\
(iii) Evaluate $\sum _ { n = 1 } ^ { 500 } u _ { n }$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q4 [3]}}