| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2014 |
| Session | June |
| Marks | 3 |
| Topic | Arithmetic Sequences and Series |
| Type | Find term or common difference |
| Difficulty | Easy -1.3 This is a straightforward arithmetic progression question requiring only direct application of standard formulas (nth term and sum formulas) with minimal algebraic manipulation. Part (iii) involves a simple linear transformation of the sum already found in part (ii), making it routine rather than requiring any problem-solving insight. |
| Spec | 1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
(i) 68
B1 [1]
(ii) $S_{15} = 7.5 \times (2 \times 5 + 14 \times 7)$
$= 810$
M1 Attempting to use correct formula
A1 [2]
(iii) New series with $a = 11$ and $d = 14$
M1 Either identified explicitly, used in formula or just listing new terms (could be $a$ & $l$)
$S_{15} = 7.5 \times (2 \times 11 + 14 \times 14)$
$= 1635$
M1
A1 [3]
**OR**
$\sum_1^{15} 2x_n + 1 = 2\sum_1^{15} x_n + 15$
M1 Allow M1M0 for $\left(2\sum_1^{15} x_n\right) + 1$
$= 2 \times 810 + 15$
$= 1635$
M1
A15 An arithmetic progression has first term 5 and common difference 7.\\
(i) Find the value of the 10th term.\\
(ii) Find the sum of the first 15 terms.
The terms of the progression are given by $x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots$.\\
(iii) Evaluate $\sum _ { n = 1 } ^ { 15 } \left( 2 x _ { n } + 1 \right)$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2014 Q5 [3]}}