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Common Difference

The 4th term ...

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

Here, $a_{4} = 11 \Rightarrow a + 3 d = 11 . . . (1)$

Also, $a_{5} + a_{7} = 34 \Rightarrow a + 4 d + a + 6 d = 34 \Rightarrow a + 5 d = 17 . . . (2)$

Subtracting (1) from (2), $2 d = 17 - 11 = 6 \Rightarrow d = 3$

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