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Given a=2,d=8,sn=90, find the n and …

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Given a=2,d=8,sn=90, find the n and a

    • Posted by Anshuman Nayak 3 years, 7 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Ayushi Gupta 3 years, 7 months ago

    Sn = n/2 (2a + (n-1)) Sn = n/2 ( 4 + 8n -8) Sn = n/2 (8n - 4) 90 = -2n + 4n^2 4n^2 - 2n - 90 = 0 2(2n^2 - n - 45 = 0) 2n^2 - n - 45 = 0 2n^2 - 10n + 9n - 45 = 0 2n(n-5) 9(n-5) = 0 (n-5) (2n + 9) = 0 "n" can't be negative or in fraction so.., n = 5

    1Thank You

    Aryan Pradhan 3 years, 7 months ago

    We know that Sn=n/2[2a+(n-1)d] Now, 90=n/2[4+(n-1)8] 90=n/2(4+8n-8) 180=n(4+8n-8) 180=n(8n-4) 180=8n^2-4n 8n^2-4n-180=0 4(2n^2-n-45)=0 2n^2-n-45=0 2n^2-10n+9n-45=0 2n(n-5)+9(n-5)=0 2n=-9,n=-9/2 n-5=0,n=5

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