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The 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64. The common difference of an AP is [[1]].

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answer is 3.

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Detailed Solution

The 5th term of an AP is 20 and the sum of its 7th and 11term is 64. The common difference of an AP is 3.
It is given that, 5th term of an AP is 20 and the sum of its 7th and 11th terms is 64.
We have to find the common difference.

a 5 = 20

The nth term of an AP is given by,

a n = a + (n − 1) d

Substitute the known values in the formula,

a 5 = 30

a + 4 d = 20

……(1)

a 7 + a 11 = 64

Substitute the known values in the formula,

a + 7 − 1 × d + a + 11 − 1 × d = 64

a + 6 d + a + 10 d = 64

a + 8 d = 32

……(2)
Solve equations (1) and (2) by subtracting (2) from (1),

a + 8 d − a − 4 d = 32 − 20

4 d = 12

d = 3

The common difference is 3.

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