Question

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

Answer 1

We know that, For an A.P.,
\(a_n = a + (n − 1) d\)
\(a_{17} = a + (17 − 1) d\)
\(a_{17} = a + 16d\)       ……. (i)
Similarly,
\(a_{10} = a + (10− 1) d\)
\(a_{10}= a + 9d\)       ……. (ii)
It is given that,
\(a_{17} − a_{10} = 7\)
\((a + 16d) − (a + 9d) = 7\)
\(7d = 7\)
\(d = 1\)

Therefore, the common difference is 1.