Answer :

Given:

t3 = 5


t7 = 9


For an A.P. the nth term is given by


tn = a + (n-1)d


where


a is the first term of the A.P.


d is the common difference


According to the problem:


t3 = a + 2d


a + 2d = 5…(i)


t7 = a + 6d


a + 6d = 9….(ii)


Subtracting equation (ii) from (i) we get


4d = 4


d = 1


Putting the value in Equation (i) we get


a + 2 = 5


a = 3


Answer: The A.P. series is 3, 4, 5, 6, 7 ….


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