Express euse0 4If Sn denotes the sum of n terms of an AP whose common

1.	Express euse0 4If Sn denotes the sum of n terms of an AP whose common difference is d and first termTind the mean of the following distribution:is a, find S,-25,-
Answer» Sn= (n/2)[ 2a + ( n -1) d]then Sn- 2Sn-1+ Sn + 2⇒ (n/2)[ 2a + ( n -1) d] - 2(n - 1)/2)[ 2a + ( n - 1 -1) d] + (n +2) / 2)[ 2a + ( n + 2 -1) d] ⇒ (1/2)[ 2an + n( n -1) d] + [ 4a(n - 1) + 2(n - 1)( n - 2) d] +[ 2a(n + 2)+ ( n + 1) (n + 2) d] ⇒ (1/2)[ 2a[ n - 2n + 2 + n + 2] + d [ n2- n - 2n2+ 6n - 4 + n2+ 3n + 2] ] ⇒ (1/2)[ 2a(4) + d(8n - 2) ]= [ 4a + (4n - 1)d]

Express euse0 4If Sn denotes the sum of n terms of an AP whose common difference is d and first termTind the mean of the following distribution:is a, find S,-25,-

Answer»

Sn= (n/2)[ 2a + ( n -1) d]then Sn- 2Sn-1+ Sn + 2⇒ (n/2)[ 2a + ( n -1) d] - 2(n - 1)/2)[ 2a + ( n - 1 -1) d] + (n +2) / 2)[ 2a + ( n + 2 -1) d]

⇒ (1/2)[ 2an + n( n -1) d] + [ 4a(n - 1) + 2(n - 1)( n - 2) d] +[ 2a(n + 2)+ ( n + 1) (n + 2) d]

⇒ (1/2)[ 2a[ n - 2n + 2 + n + 2] + d [ n2- n - 2n2+ 6n - 4 + n2+ 3n + 2] ]

⇒ (1/2)[ 2a(4) + d(8n - 2) ]= [ 4a + (4n - 1)d]