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Example 15 - Find sum of first 24 terms, an = 3 + 2n  - Examples

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
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Example 15 Find the sum of first 24 terms of the list of numbers whose nth term is given by an = 3 + 2n Given an = 3 + 2n Now 1st term = a1 = 3 + 2 (1) a = 3 + 2 a = 5 2nd term = a2 = 3 + 2 (2) = 3 + 4 = 7 3rd term = a3 = 3 + 2 (3) = 3 + 6 = 9 4th term = a4 = 3 + 2 (4) = 3 + 8 = 11 So, the series is 5, 7, 9, 11 ……… Since 7 – 5 = 2 9 – 7 = 2 11 – 9 = 2 So, difference of consecutive terms is same, So, it is an AP We need to find sum of first 24 terms We use the formula Sn = 𝑛/2[2𝑎+(𝑛−1)𝑑] Where n = 24, a = 5 d = 7 – 5 = 2 Putting these values in formula Sum = 𝑛/2[2𝑎+(𝑛−1)𝑑] = 24/2[2×5+(24−1)2] = 12 [10+(23)(2)] = 12 [10+46] = 12 ×56 = 672 Hence, sum of 24th terms = 672

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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