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If a=2 and d=8 and Sn=90 . Find n and an. |
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Answer» Sn=n/2(2a+(n-1)d)90=n/2(4+8n-8)180=n(8n-4)8n²-4n-1802(4n²-n-45)n=-9/2,n=5 90 = n/2(4+(n-1)8)180= n(4+8n -8)180= -4n+8n^28n^2-4n -180 =0Solve it for n Sn = 90Sn = n/2 [ 2a + (n - 1)d]90 = n/2 [ 2 x 2 + (n - 1)8]180/n = 4 + 8n - 8180/n = 8n - 4180 = 8n^2 - 4n{tex}8n^2 - 4n - 180 = 0{/tex}{tex}2n^2 - n - 45 = 0{/tex}{tex}2n^2 - 10n + 9n - 45 = 0{/tex}2n( n - 5) + 9( n - 5) = 0(2n + 9)(n - 5) = 0n = -9/2 or n = 5But n cannot be negative.So, n = 5an = a + (n - 1)da5 = 2 + (5-1)8a5 = 2 + 4 x 8a5 = 2 + 32 = 34 N=5,an=34;if n=9/2,an=38 |
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