Question

The 17^th term of an AP exceeds its 10^th term by 7. Find the common difference.

Answer 1

For an A.P., the n-th term is given by \(a_n = a + (n − 1) d\).
Thus, \(a_{17} = a + (17 − 1) d\), which simplifies to \(a_{17} = a + 16d\)……. (i).
Similarly, \(a_{10} = a + (10− 1) d\), which simplifies to \(a_{10}= a + 9d\)……. (ii).
Given that \(a_{17} − a_{10} = 7\), substituting the expressions from (i) and (ii) gives \((a + 16d) − (a + 9d) = 7\).
This simplifies to \(7d = 7\), and therefore \(d = 1\).

The common difference is 1.