Question

What is the sum of the first 11 terms of an A.P. if the 4th is 11 and the 7th is -4

Answer 1

Hii !!

Given :-

4th term = 11

a + 3d = 11

a = ( 11 - 3d ) ---------(1)

And,

7th term = -4

a + 6d = -4 ----------(2)

Putting the value of a in equation (2) , we get

a + 6d = -4

11 - 3d + 6d = -4

3d + 11 = -4

3d = -4 - 11

d = -5

Putting the value of d in equation (1) , we get

a = 11 - 3d = 11 - 3 × -5

a = 11 + 15

a = 26.

First term = 26

And,

Common difference ( d ) = -5

Therefore,

Sn= n/2 × [ 2a+ ( n - 1 ) × d ]

S11 = 11/2× [ 2 × 26 + ( 11 - 1 ) × -5 ]

S11 = 11/2 × ( 52 + 10 × -5 )

S11 = 11/2 × ( 52 - 50)

S11 = 11/2 × 2


S11 = 11