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Question
The 25th term of an A.P. exceeds its 9th term by 16. Find its common difference.
Solution
nth term of an A.P. is given by tn= a + (n – 1) d.
`\implies` t25 = a + (25 – 1)d = a + 24d
And t9 = a + (9 – 1)d = a + 8d
According to the condition in the question, we get
t25 = t9 + 16
`\implies` a + 24d = a + 8d + 16
`\implies` 16d = 16
`\implies` d = 1
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