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Example 8 - Find 11th term from last term: 10, 7, 4, .. -62  - Finding nth term from end

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
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Example 8 Find the 11th term from the last term (towards the first term) of the AP : 10, 7, 4, . . ., – 62. AP is 10,7,4, ……….,–62 Here a = 10 d = 7 – 10 = – 3 First lets find which term is – 62 Let an = – 62 a + (n – 1) d = – 62 Putting values 10 + (n – 1) ( –3) = – 62 10 + n (–3) – 1(–3) = – 62 10 – 3n + 3 = –62 13 – 3n = –62 –3n = –13 – 62 –3n = –75 n = (−75)/(−3) n = 25 We need to find out 11th term from the last term Last term = 25th Second last term = 25 – 1 = 24th Third last term = 25 – 2 = 23rd And so, on So, 11th from last term = (25 – 10)th term . = 15th term So, we need to find out a15 an = a + (n – 1) d Putting values a15 = 10 + (15 – 1) ( – 3) a15 = 10 + (14) ( – 3) = 10 – 42 = – 32 So the 11th term from the Last = 15th term from the First = – 32

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