Question

The number of terms in the A.P. \(2,\,6,\,10,\,14,\,\ldots,\,82\) is

• A. \(15\)
• B. \(21\)
• C. \(20\)
• D. \(22\)

Hint:

When first term \(a\), last term \(l\) and \(d\) are known: \(n=\dfrac{l-a}{d}+1\).

Answer 1

The Correct Option is B

Step 1: Identify \(a,d,l\).
\(a=2,\ d=4,\ l=82\).
Step 2: Use last-term formula.
\(l=a+(n-1)d \Rightarrow 82=2+(n-1)\cdot 4\).
Step 3: Solve for \(n\).
\(80=4(n-1)\Rightarrow n-1=20\Rightarrow n=21\).