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Question
Determine the A.P. whose third term is 5 and the seventh term is 9.
Solution
Given, T3 = 5 and T7 = 9
We know that the nth term of an A.P. is
Tn = a + (n – 1)d
∴ 5 = a + 4d ...(i)
And 9 = a + 6d ...(ii)
Subtracting equation (i) from equation (ii),
–4 = –2d
⇒ d = 2
Put d = 2 in equation (i),
5 = a + 4(2)
⇒ a = 5 – 8
⇒ a = –3
So, the required A.P. is –3, –1, 1, 3, 5, 7, 9, .........
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