Sum of specific range of terms

Find the sum of terms from position p to position q, typically using S_q - S_(p-1) or summing the subsequence directly.

6 questions · Moderate -0.3

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CAIE P1 2024 June Q7
7 marks Standard +0.3
7 The first term of an arithmetic progression is 1.5 and the sum of the first ten terms is 127.5 .
  1. Find the common difference.
  2. Find the sum of all the terms of the arithmetic progression whose values are between 25 and 100 .
OCR MEI C2 2006 June Q6
5 marks Moderate -0.8
6 A sequence is given by the following. $$\begin{aligned} u _ { 1 } & = 3 \\ u _ { n + 1 } & = u _ { n } + 5 \end{aligned}$$
  1. Write down the first 4 terms of this sequence.
  2. Find the sum of the 51st to the 100th terms, inclusive, of the sequence.
OCR C2 2015 June Q7
11 marks Standard +0.3
7 In an arithmetic progression the first term is 5 and the common difference is 3 . The \(n\)th term of the progression is denoted by \(u _ { n }\).
  1. Find the value of \(u _ { 20 }\).
  2. Show that \(\sum _ { n = 10 } ^ { 20 } u _ { n } = 517\).
  3. Find the value of \(N\) such that \(\sum _ { n = N } ^ { 2 N } u _ { n } = 2750\).
AQA C2 2005 January Q3
6 marks Moderate -0.3
3 An arithmetic series has fifth term 46 and twentieth term 181.
    1. Show that the common difference is 9 .
    2. Find the first term.
  2. Find the sum of the first 20 terms of the series.
  3. The \(n\)th term of the series is \(u _ { n }\). Given that the sum of the first 50 terms of the series is 11525 , find the value of $$\sum _ { n = 21 } ^ { 50 } u _ { n }$$
AQA C2 2008 January Q2
5 marks Moderate -0.8
2 The arithmetic series $$51 + 58 + 65 + 72 + \ldots + 1444$$ has 200 terms.
  1. Write down the common difference of the series.
  2. Find the 101st term of the series.
  3. Find the sum of the last 100 terms of the series.
AQA C2 2016 June Q4
10 marks Moderate -0.3
4 An arithmetic series has first term \(a\) and common difference \(d\).
The sum of the first 21 terms is 168 .
  1. Show that \(a + 10 d = 8\).
  2. The sum of the second term and the third term is 50 . The \(n\)th term of the series is \(u _ { n }\).
    1. Find the value of \(u _ { 12 }\).
    2. Find the value of \(\sum _ { n = 4 } ^ { 21 } u _ { n }\).