how many terms of the A. P 11/3,4,13/3...must be added to Obtain the sum 216
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A. P. = 11 / 3, 4, 13 /3.....
a, First term = 11 /3
a2, Second term = 4
Common difference, d = a2 - a = 4 - 11/3
d = ( 12 - 11 ) / 3 = 1 / 3
For sum of 216,
Sn = n / 2 [ 2a + ( n - 1 ) d]
216 = n / 2 [ 2 × 11 /3 + ( n - 1 ) 1 /3 ]
432 = n [ 22/3 + n /3 - 1 / 3]
432 = n [ 21 /3 + n /3 ]
432 = n [( 21 + n) / 3 ]
432 × 3 = 21n + n ^2
0 = n^2 + 21n - 1296
0 = n^2 + 48n - 27 n - 1296
0 = n ( n + 48 ) - 27 ( n + 48 )
0 = ( n - 27 ) ( n + 48 )
( n - 27 ) = 0, ( n + 48 ) = 0
n = 27, - 48
So, Number of terms needed = 27.
a, First term = 11 /3
a2, Second term = 4
Common difference, d = a2 - a = 4 - 11/3
d = ( 12 - 11 ) / 3 = 1 / 3
For sum of 216,
Sn = n / 2 [ 2a + ( n - 1 ) d]
216 = n / 2 [ 2 × 11 /3 + ( n - 1 ) 1 /3 ]
432 = n [ 22/3 + n /3 - 1 / 3]
432 = n [ 21 /3 + n /3 ]
432 = n [( 21 + n) / 3 ]
432 × 3 = 21n + n ^2
0 = n^2 + 21n - 1296
0 = n^2 + 48n - 27 n - 1296
0 = n ( n + 48 ) - 27 ( n + 48 )
0 = ( n - 27 ) ( n + 48 )
( n - 27 ) = 0, ( n + 48 ) = 0
n = 27, - 48
So, Number of terms needed = 27.
archit124:
u can do in easy way plz
Easy way..? It's not very tough.
kk
Answered by
1
Answer:
27
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