# Question 8:

## Part (a):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $238 = a + kd$ **or** $108 = a + kd$ with any values for $k$ | M1 | Any non-zero integer value for $k$ |
| $238 = a + (14)d$ or $108 = a + (24)d$ or $"d" = \pm 13$ | A1 | One of these correct; $"d" = \pm 13$ can come from equations like $238 = a + (13)d$ or $108 = a + (23)d$ |
| $238 = a + (14)d$ **and** $108 = a + (24)d$ | A1 | Both correct simultaneously |
| Solves simultaneous equations to obtain $a = 420$ | M1, A1 | Finds value of $a$ by solving pair of simultaneous equations in $a$ and $d$ |

**Alternative (method of differences):**

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{238-108}{10}$ or $\frac{108-238}{10}$ | 1st M1 | |
| $\pm 13$ | 1st A1 | |
| $238 + 13 \times 14$ or $108 + 13 \times 24$ | 2nd A1 | Achieved after award of next mark; scored as third mark on e-pen |
| Sight of $238 + {'}k{'} \times d$ or $108 + {'}k{'} \times d$ with any non-zero integer $k$ and their $d$ | 2nd M1 | |
| Achieves 420 | 3rd A1 | |

## Part (b):

| Answer/Working | Mark | Guidance |
|---|---|---|
| Uses $\frac{25}{2}(2 \times a + (25-1) \times "-13")$ **or** $\frac{25}{2}(a + 108)$ to obtain 6600 | M1, A1 | Uses correct sum formula $S = \frac{n}{2}(2a + (n-1)d)$ with $n=25$ and their $a,d$; alternatively $S = \frac{n}{2}(a+l)$ with $n=25, l=108$ and their $a$ |

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