Question

The fourth term of an AP is 11 .The sum of fifth and seventh terms of the AP is 34.Find it's common difference.

Answer 1

EXPLANATION.

• GIVEN

Fourth term of an Ap = 11

sum of 5th and 7th term of an Ap = 34

FIND IT'S COMMON DIFFERENCE.

according to the question,

Nth term of an Ap

=> An = a + ( n - 1 ) d

Case = 1

=> 4th term of an Ap = 11

=> a + 3d = 11 .......(1)

Case = 2

=> 5th and 7th term = 34

=> a + 4d + a + 6d = 34

=> 2a + 10d = 34

=> a + 5d = 17 ......(2)

From equation (1) and (2) we get,

=> -2d = -6

=> d = 3

put the value of d = 3 in equation (1)

we get,

=> a + 3(3) = 11

=> a = 2

Therefore,

common difference = 3

first term = 2