Given a = 2 , d = 8, s n = 90, find n and a n
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Sn = n/2{2a +(n-1)d}
90 = n/2{4 +(n-1)8}
90 =n/2{4+8n-8}
90 =n/2{8n-4}
90 =n/2×2(4n-2)
90 =n(4n-2)
90/2 =n(2n-1)
45 = 2n^2-n
2n^2-n-45=0
2n^2-10n+9n-45=0
2n(n-5)+9(n-5)=0
Hence
n-5=0
n=5
Also n cannot be negative
An=a+(n-1)d
=2+(5-1)8
=2+4×8
=34
90 = n/2{4 +(n-1)8}
90 =n/2{4+8n-8}
90 =n/2{8n-4}
90 =n/2×2(4n-2)
90 =n(4n-2)
90/2 =n(2n-1)
45 = 2n^2-n
2n^2-n-45=0
2n^2-10n+9n-45=0
2n(n-5)+9(n-5)=0
Hence
n-5=0
n=5
Also n cannot be negative
An=a+(n-1)d
=2+(5-1)8
=2+4×8
=34
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