# In an AP : given a=2 , d=8 , Sn=90 ,find n and An .this is a problem from the chapter arithematic progressions from the 10th NCERT textbook

Given: a=2 , d=8 , Sn=90

Sn = n/2 {2a + (n-1) d}

90 = n/2{4+(n-1)8}

180 = n(8n - 4)

45 = n(2n-1)

2n2 - n -45 =0

2n2 - 10n + 9n -45 =0

2n(n-5) + 9 (n-5)=0

(n-5)(2n+9)=0

n = -9/2 (not possible )

n = 5

T(n) = a +(n-1)d

= 2 +(n-1) 8

= 8n - 6

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