In the Ap 3,7,11.......sum of first n terms is 253.find the value of n?
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d = 4
a = 3
Sn = 253
n = ?
Sn = n/2 [ 2a + (n-1)d ]
253 = n/2 [ 2×3 + (n-1)4]
253 = n ( 3 + 2n -2 )
253 = 2n^{2} + n
2n^{2} + n - 253 = 0
2n^{2} - 22n + 23n - 253 = 0
2n ( n -11 ) + 23 (n -11) = 0
( 2n + 23 ) ( n - 11 ) = 0
n = 11 [ as n cannot be in negative ]
Your answer is n = 11
d = 4
a = 3
Sn = 253
n = ?
Sn = n/2 [ 2a + (n-1)d ]
253 = n/2 [ 2×3 + (n-1)4]
253 = n ( 3 + 2n -2 )
253 = 2n^{2} + n
2n^{2} + n - 253 = 0
2n^{2} - 22n + 23n - 253 = 0
2n ( n -11 ) + 23 (n -11) = 0
( 2n + 23 ) ( n - 11 ) = 0
n = 11 [ as n cannot be in negative ]
Your answer is n = 11
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