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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 from the subsequent choices.

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answer is B.

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Detailed Solution

It is given that the 4th term of an AP is 11.
The sum of the 5th and 7th terms of this AP is 34.
We have to find the common difference.

a 4 = 11 a 5 + a 7 = 34

The nth term of an AP is given by,

a n = a + n − 1 × d

Now, substitute the formula for the 4th term of an AP,

a 4 = a + (4 − 1) d a 4 = a + 3 d a + 3 d = 11 a = 11 − 3 d

.
Similarly,

a 5 = a + 4 d a 7 = a + 6 d

Now, the sum of the fifth and seventh term is 34, so,

a 5 + a 7 = a + 4 d + a + 6 d 34 = 2 a + 10 d 17 = a + 5 d

Substitute a = 11 – 3d in the above equation,

17 = 11 − 3 d + 5 d 2 d = 17 − 11 2 d = 6 d = 3

The value of common difference is 3.
Hence, option 2) is correct.

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