Sum of arithmetic progressions

Question

The sum of 3rd and 9th term of ap is 8.find the sum of the first 11terms

Answer 1

Given t3 + t9 = 8

But,   t3  =  a + 2d ---------> (1)

         t9  =  a + 8d -------------> (2)

Add Equations (1) and (2)

        t3  =  a + 2d

        t9  =  a + 8d 

__________________

t3 + t9  =  2a + 10d

       8   =  2a + 10d ------------> (3)            [ Since t3 + t9 = 8 ]

Sum of the numbers in AP 

Sn  =  n/2 [ 2a + (n - 1)d ] --------> (4)

Substitute n =11 in Eq (4)

S11  =  11/2 [ 2a + (11 - 1)d ]

S11  =  11/2 [ 2a + 10d ] 

S11  =  11/2 [ 8 ]                                   [ Since 2a + 10d = 8 ]

s11  =  44.

Answer :

The sum of First 11 terms is 44