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Question
The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.
Solution
Let the first term and common difference of AP are a and d, respectively.
According to the question,
a5 + a7 = 52 and a10 = 46
⇒ a + (5 – 1)d + a + (7 – 1)d = 52 ...[∵ an = a + (n – 1)d]
And a + (10 – 1)d = 46
⇒ a + 4d + a + 6d = 52
And a + 9d = 46
⇒ 2a + 10d = 52
And a + 9d = 46
⇒ a + 5d = 26 ...(i)
a + 9d = 46 ...(ii)
On subtracting equation (i) from equation (ii), we get
4d = 20
⇒ d = 5
From equation (i),
a = 26 – 5(5) = 1
So, required AP is a, a + d, a + 2d, a + 3d,...
i.e., 1, 1 + 5, 1 + 2(5), 1 + 3(5),...
i.e., 1, 6, 11, 16,...
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