Question

Which term of the AP: 21, 42, 63, 84 ... is 210?

• A. \(9^{th}\)
• B. \(10^{th}\)
• C. \(11^{th}\)
• D. \(12^{th}\)

Hint:

Find \(a\) and \(d\), then solve \(a + (n - 1)d = 210\) for \(n\).

Answer 1

The Correct Option is B

Step 1: Notice the pattern:
Every number in the list is a multiple of 21: \(21 \times 1,\ 21 \times 2,\ 21 \times 3,\ 21 \times 4, \ldots\)
So the \(n\)th term is simply \(21n\).

Step 2: Set up the equation:
We want the term that is 210, so \(21n = 210\).

Step 3: Solve:
\[ n = \frac{210}{21} = 10 \]

Step 4: Check the options:
9th term: \(21 \times 9 = 189\). 10th term: \(21 \times 10 = 210\). 11th term: \(21 \times 11 = 231\). 12th term: \(21 \times 12 = 252\).
Only the 10th term equals 210, so (B) is correct and the others are wrong.

Final Answer:
210 is the 10th term, which is option (B). \[ \boxed{10^{th}} \]