the sum of 5th and 7th term of an a.p is 52 and 10th term is 46 find common difference(with steps)
GIVEN : the sum of 5th and 7th term of an A.P is 52.
an = a+(n-1)d
a5 = 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.