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If the sum of first four terms of an AP is 40 and that of first 14 terms is 280 . Find the sum of its first n terms ?? |
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Answer» -step explanation:Given : .First Form TERM A P is 40 First 14 term 280 Find : . SUM Of n term Solution : . We know Sum of n term = n/2 [ 29 + ( n - 1 ) d ] Sum Of 4 = 40 and Sum Of 14 = 280 4/2 [ 29 + ( 4 - 1 ) d ] 40 , 14/2 [ 29 + ( 14 - 1 ) d ] = 280 ( 29 + 3d ) = 40/2 , 7 ( 29 + 13d ) = 280 29 + 3d = 20 ( i ) 29 + 13d = 40 ( II ) From Equation ( i ) and ( ii ) 29 + 3d = 20 29 + 13d = 40 - 10d = - 20 d = - 20/-10 d = 2 Putting value d = 2 From ( i ) we get a = 7 Sum Of n term = n/2 [ 2 ( 7 ) + ( n - 1 ) 2 ] Sum of n term = n/2 2 [ 7 + n - 1 ] Sum of n term = n ( n + 6 ) Sum of n term n ( n + 6 ) or n^2 + 6 n |
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