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MAO 6.10 Aritm. rekke

MAO 6.10 Aritm. rekke. Skal finne n når a 1 =2, d=3 og S n =100. a n = a 1 + d(n-1) ==> a n = 2+ 3(n-1). S n = 0,5*(a 1 + a n )*n ==> S n = 0,5*(2 + a n )*n. uttrykket for a n settes inn i uttrykket for S n:. S n = 0,5*(2 + (2+3(n-1)))*n = 100. S n = 0,5*(2n + 2n+3n 2 -3n) = 100.

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MAO 6.10 Aritm. rekke

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  1. MAO 6.10 Aritm. rekke Skal finne n når a1=2, d=3 og Sn =100 an = a1 + d(n-1) ==> an = 2+ 3(n-1) Sn = 0,5*(a1 + an)*n ==> Sn = 0,5*(2 + an)*n uttrykket for an settes inn i uttrykket for Sn: Sn = 0,5*(2 + (2+3(n-1)))*n = 100 Sn = 0,5*(2n + 2n+3n2-3n) = 100 0,5*n +1,5*n2 - 100 = 0==> 3n2 +n- 200 = 0 ==> n= 8 (neg. løsn. forkastes)

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