Find the number of terms in the A.P.
4, 13, 22, 31, ..., 184
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 21
The \(n\)th term of an A.P. is \(a_n=a+(n-1)d\), so the number of terms comes from setting the last term equal to 184.
First term \(a=4\), common difference \(d=13-4=9\)
Last term: \(4+(n-1)\times9=184\)
\((n-1)\times9=180\), so \(n-1=20\)
Number of terms \(n=21\)
Tip: 20 (Option 3) is the number of gaps of 9 between 4 and 184; the number of terms is one more than the number of gaps.