The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
1
Step 1: Recall the nth term formula of an AP.
For an arithmetic progression (AP), the nth term is given by:
\[a_n = a + (n - 1)d\]
where \(a\) is the first term and \(d\) is the common difference.
Step 2: Write expressions for the 10th and 17th terms.
10th term:
\[a_{10} = a + 9d\]
17th term:
\[a_{17} = a + 16d\]
Step 3: Use the given condition.
The 17th term exceeds the 10th term by 7. So:
\[a_{17} - a_{10} = 7\]
Substitute the expressions:
\[(a + 16d) - (a + 9d) = 7\]
Step 4: Simplify the equation.
\[a + 16d - a - 9d = 7\]
\[7d = 7\]
Step 5: Solve for \(d\).
\[d = \dfrac{7}{7} = 1\]
Conclusion: The common difference of the AP is 1.