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Question
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference
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Solution
Let a be the first term and d be the common difference of the AP. Then,
a4 = 11
⇒ a+ (4-1) d = 11 [ an = a + (n-1) d]
⇒ a+3d = 11 ..............(1)
Now
a5 + a7 = 34 ( Given)
⇒ (a 4d) +(a + 6d ) = 34
⇒ 2a + 10d = 34
⇒ a+ 5d = 17 ...........(2)
From (1) and (2), we get
11-3d + 5d = 17
⇒ 2d = 17 - 11 = 6
⇒ d = 3
Hence, the common difference of the AP is 3.
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