Find the value of the common difference of this sequence.

Calculate the sum of the first 10 terms of this sequence.

Find the number of terms in this sequence.

\(d = 321 - 326\) (or equivalent)

\( =  - 5\)     (A1)(A1)     (C2)

Note: Award (A1) for negative sign. (A1) for 5.

[2 marks]

\({S_{10}} = \frac{{10}}{2}(2(326) + 9( - 5))\)     (M1)

Notes: Award (M1) for correctly substituted formula. Follow through from part (a).

OR

\({u_{10}} = 281\)

\({S_{10}} = \frac{{10}}{2}(326 + 281)\)     (M1)

Note: Award (M1) for correctly substituted formula, not for finding 281.

OR

If a list is seen award (M1) for the correct list of 10 terms consistent with their \(d\).     (M1)

\( = 3035\)     (A1)(ft)     (C2)

Note: If \(d = 5\) final answer is 3485. Follow through from part (a). No follow through if list used.

[2 marks]

\(191 = 326 + (n - 1)( - 5)\)     (or equivalent)     (M1)

Notes: Award (M1) for correctly substituted formula. Follow through from part (a).

OR

If a list is seen award (M1) for the complete and correct list of terms or complete list of terms consistent with their \(d\).     (M1)

\(n = 28\)     (A1)(ft)     (C2)

Note: \(n\) must be a positive integer. Follow through from part (a). No follow through if list used.

[2 marks]

At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. The most common error was in part (a) where \(5\), rather than \( - 5\) resulted in a lost mark. Recovery was, of course, possible in the remainder of the question. Further errors occurred where lists, rather than formulae, were used in parts (b) and (c). Using properly constructed and accurate lists were not in themselves penalized; arithmetical errors seen in a significant number of lists given by candidates, however, were penalized.

At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. The most common error was in part (a) where \(5\), rather than \( - 5\) resulted in a lost mark. Recovery was, of course, possible in the remainder of the question. Further errors occurred where lists, rather than formulae, were used in parts (b) and (c). Using properly constructed and accurate lists were not in themselves penalized; arithmetical errors seen in a significant number of lists given by candidates, however, were penalized.

At whatever ability, there were good attempts by all candidates on this question with an overwhelming majority scoring half marks or more. The most common error was in part (a) where \(5\), rather than \( - 5\) resulted in a lost mark. Recovery was, of course, possible in the remainder of the question. Further errors occurred where lists, rather than formulae, were used in parts (b) and (c). Using properly constructed and accurate lists were not in themselves penalized; arithmetical errors seen in a significant number of lists given by candidates, however, were penalized.