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Sn = 90
Sn = n/2 [ 2a + (n - 1)d]
90 = n/2 [ 2 x 2 + (n - 1)8]
180/n = 4 + 8n - 8
180/n = 8n - 4
180 = 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) = 0
n = -9/2 or n = 5
But n cannot be negative.
So, n = 5
an = a + (n - 1)d
a5 = 2 + (5-1)8
a5 = 2 + 4 x 8
a5 = 2 + 32 = 34
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Rohit Gupta 6 years ago
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