• Math

  Arithmetic fun

  Posted by Shishank on June 24, 2023 at 11:17 pm

  How many terms of the A.P. 30,27,24,21,… should be taken so that their sum is zero?

  Rajesh replied 3 months ago 2 Members · 1 Reply

  • funmath
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  Rajesh

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  June 25, 2023 at 5:02 pm

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  Given that AP is 27, 24, 21 …

  a1 = 30 ;a2=27; a3 = 24 and d =a2-a1= 27- 30 = (-3) ; sn =0 (given )

  We know that

  Sn=n/2 [2a+(n−1)d]

  Since the sum is 0,

  n/2[2×30+(n−1)(−3)]=0

  n(60−3n+3)=0

  n(60−3n)=0

  n=0 and 60−3n=0

  60=3n

  n = 60/3

  n = 20

  ∴n=0 and n=20

  Since the number of terms cannot be equal to 0 so number of terms (n) = 20

  • This reply was modified 3 months ago by  Rajesh Saini. Reason: Type mistake

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