Find term or common difference

Given some terms of an arithmetic progression, find the first term, common difference, or a specific term using the formula a + (n-1)d.

31 questions · Moderate -0.7

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Edexcel Paper 2 2021 October Q1
4 marks Easy -1.2
  1. In an arithmetic series
  • the first term is 16
  • the 21 st term is 24
    1. Find the common difference of the series.
    2. Hence find the sum of the first 500 terms of the series.
OCR MEI Paper 2 2020 November Q5
3 marks Moderate -0.8
5 The first \(n\) terms of an arithmetic series are \(17 + 28 + 39 + \ldots + 281 + 292\).
  1. Find the value of \(n\).
  2. Find the sum of these \(n\) terms.
Edexcel C1 Q7
11 marks Moderate -0.3
7. (a) An arithmetic series has a common difference of 7 . Given that the sum of the first 20 terms of the series is 530 , find
  1. the first term of the series,
  2. the smallest positive term of the series.
    (b) The terms of a sequence are given by $$u _ { n } = ( n + k ) ^ { 2 } , \quad n \geq 1 ,$$ where \(k\) is a positive constant.
    Given that \(u _ { 2 } = 2 u _ { 1 }\),
  3. find the value of \(k\),
  4. show that \(u _ { 3 } = 11 + 6 \sqrt { 2 }\).
Edexcel C1 Q8
10 marks Moderate -0.8
8. (a) The first and third terms of an arithmetic series are 3 and 27 respectively.
  1. Find the common difference of the series.
  2. Find the sum of the first 11 terms of the series.
    (b) Find the sum of the integers between 50 and 150 which are divisible by 8 .
AQA C2 2007 June Q4
7 marks Moderate -0.8
4 An arithmetic series has first term \(a\) and common difference \(d\).
The sum of the first 29 terms is 1102.
  1. Show that \(a + 14 d = 38\).
  2. The sum of the second term and the seventh term is 13 . Find the value of \(a\) and the value of \(d\).
OCR MEI C2 2008 June Q8
5 marks Moderate -0.3
8 The 11th term of an arithmetic progression is 1 . The sum of the first 10 terms is 120 . Find the 4th term. [5]