Given d=5,S9=75find a and a9
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S9 = 75 , d = 5 , a = ? , a9 = ?
We know that :
Sn = n/2 ( 2a + ( n - 1 ) d )
S9 = 9 / 2 ( 2a + ( 9 - 1 ) 5 )
75 = 9/2 ( 2a + (8) 5 )
75 * 2 / 9 = 2a + 40
150 / 9 = 2a + 40
2a = 150 / 9 - 40
2a = 50 / 3 - 40
2a = 50 - 120 / 3
2a = -70/3
a = - 70 / 3 *2
a = -35 / 3
an = a + ( n - 1 ) d
a9 = -35 / 3 + ( 9 - 1 ) 5
a9 = -35 / 3 + (8) 5
a9 = -35/3 + 40
a9 = -35 + 120 / 3
a9 = 85 / 3
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