Determine the AP

Given:

t₃ = 5

t₇ = 9

For an A.P. the n^th term is given by

t_n = 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 ….