Which term of the AP: 3, 8, 13, 18, ... is 78?
16th term
Step 1: Identify the first term and common difference.
The AP is: 3, 8, 13, 18, ...
So, first term \(a = 3\).
Common difference \(d = 8 - 3 = 5\).
Step 2: Use the general term formula of an AP.
The \(n\)th term of an AP is:
\[a_n = a + (n - 1)d\]
We are told \(a_n = 78\). Substitute the values:
\[78 = 3 + (n - 1) \cdot 5\]
Step 3: Solve for \(n\).
Subtract 3 from both sides:
\[75 = 5(n - 1)\]
Divide by 5:
\[15 = n - 1\]
Add 1 to both sides:
\[n = 16\]
Conclusion: The term 78 appears as the 16th term of the AP.