Find the sum of the series 51+50+49...............+21
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★ ARITHMETIC PROGRESSION ★
We can invert the same to obtain the results :
Hence , series will be :
21 + 22 + 23 + ... + 51
a = 21
d = 22 - 21 = 1
T( n ) = a + (n - 1)d = 51
21 + n - 1 = 51
n + 20 = 51
n = 51 - 20 = 31
Now , summation of the series :
S(n) = n/2 [ 2a + ( n - 1 )d ]
31 /2 [ 2 ( 21 ) + (31 - 1) ]
31/2 [ 42 + 30 ] = 31/2 [ 72 ]
= 1116
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We can invert the same to obtain the results :
Hence , series will be :
21 + 22 + 23 + ... + 51
a = 21
d = 22 - 21 = 1
T( n ) = a + (n - 1)d = 51
21 + n - 1 = 51
n + 20 = 51
n = 51 - 20 = 31
Now , summation of the series :
S(n) = n/2 [ 2a + ( n - 1 )d ]
31 /2 [ 2 ( 21 ) + (31 - 1) ]
31/2 [ 42 + 30 ] = 31/2 [ 72 ]
= 1116
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