Question

The 4th term of an AP is 11. Sum of the 5th &7th term is 34. Find its common difference.

Answer 1

Solution :

Let a , d are first term and common

difference of an A.P

i ) 4th term = 11

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

ii ) a5 + a7 = 34

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

=> 2a + 10d = 34

Divide each term with 2 , we get

a + 5d = 17 ----( 2 )

subtract equation ( 1 ) from ( 2 ) , we

get

2d = 6

=> d = 6/2

=> d = 3

Substitute d = 3 in equation ( 1 ), we

get

a + 3 × 3 = 11

=> a + 9 = 11

=> a = 11 - 9

=> a = 2

Therefore ,

d = 3 , a = 2

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