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Example 13 - How many terms of AP: 24, 21, 18 ... must - Examples

  1. Chapter 5 Class 10 Arithmetic Progressions
  2. Serial order wise
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Example 13 How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78? AP is 24,21,18,โ€ฆโ€ฆโ€ฆ Sum = ๐‘›/2[2๐‘Ž+(๐‘›โˆ’1)๐‘‘] Here, a = 24 d = 21 โ€“ 24 = โ€“ 3 Sum = Sn = 78 We have to find value of n Putting these values in equation Sum = ๐‘›/2[2๐‘Ž+(๐‘›โˆ’)๐‘‘] 78 = ๐‘›/2[2ร—24+(๐‘›โˆ’1)(โˆ’3)] 78 ร—2=๐‘›[48+(๐‘›โˆ’1)(โˆ’3)] 156 = n [ 48 โ€“ 3n + 3] 156 = n [ 51 โ€“ 3n] 156 = 51n โ€“ 3n2 156 = 51n โ€“ 3n2 3n2 โ€“ 51n + 156 = 0 Dividing the equation by 3 3๐‘›2/3โˆ’51๐‘›/3+156/3=0 n2 โ€“ 17n + 52 = 0 We factorize by splitting the middle term n2 โ€“ 13n โ€“ 4n + 52 = 0 n (n โ€“ 13) โ€“ 4 (n โ€“ 13) = 0 (n โ€“ 13) (n โ€“ 4) = 0 So, n = 13, n = 4 Since, both values are positive natural number. So either of them can be taken .

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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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