the sum of 5th and 7th term of an a.p is 52 and 10th term is 46 find common difference(with steps)

Chandrika Bhosge
From Kendriya Vidyalya Gulbarga, added an answer, on 7/1/14

8 helpful votes in Math
GIVEN : the sum of 5th and 7th term of an A.P is 52.

a_{n} = a+(n-1)d

a_{5 }= a+(5-1)d

5th term = a+4d ..........1

similarly, a+6d.....................2

solving eqn. 1 and 2

(a+4d) + (a+6d) = 52

a+4d+a+6d =52

2a+10d = 52 ..........3

taking 2 as common in eqn. 3 we get,

2(a+5d) = 52

a+5d = 52/2

a+5d = 26.................4

now given , 10th term = 46

ie, 10th term = a+9d = 46...................5

solving eqn.4 and 5 we get,

a+9d = 46

a+5d = 26

on subtraction

a+9d = 46

-a-5d = -26

'a' gets cancel.

we get, 4d = 20

d = 20/4

d = 5.

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