| Exam Board | Edexcel |
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| Module | C12 (Core Mathematics 1 & 2) |
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| Year | 2015 |
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| Session | January |
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| Topic | Arithmetic Sequences and Series |
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5. (a) Prove that the sum of the first \(n\) terms of an arithmetic series is given by the formula
$$S _ { n } = \frac { n } { 2 } [ 2 a + ( n - 1 ) d ]$$
where \(a\) is the first term of the series and \(d\) is the common difference between the terms.
(b) Find the sum of the integers which are divisible by 7 and lie between 1 and 500