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Question
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
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Solution
In an A.P., 17th term is 7 more than its 10th term. ...(Given)
The formula for nth term of an A.P. is tn = a + (n − 1)d
The 10th term can be written as,
t10 = a + (10 − 1)d
t10 = a + 9d
The 17th term can be written as,
t17 = a + (17 − 1)d
t17 = a + 16d
Now, according to the question,
t17 = 7 + t10
Substituting the value of t17 and t10 in the above equation,
∴ a + 16d = 7 + a + 9d
∴ 16d = 7 + 9d
∴ 16d − 9d = 7
∴ 7d = 7
∴ d = `7/7` = 1
Hence, the common difference of the given AP is 1.
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