Question

In the series 3, 9, 15, 21, _____, what is the ²⁰_th term?

• A. 100
• B. 107
• C. 112
• D. 117

Hint:

To find any term in an arithmetic progression, you need the first term and the common difference. The formula $a_n = a_1 + (n - 1)d$ is fundamental for these types of problems.

Answer 1

The Correct Option is D

Step 1: Identify the type of series.
The difference between consecutive terms is:
$9 - 3 = 6$
$15 - 9 = 6$
$21 - 15 = 6$
Since the difference between consecutive terms is constant, the series is an arithmetic progression (A.P.) with a common difference $d = 6$. Step 2: Identify the first term and the common difference.
The first term $a_1 = 3$ and the common difference $d = 6$. Step 3: Use the formula for the $n^{th$ term of an A.P.}
The formula for the $n^{th}$ term of an arithmetic progression is: $a_n = a_1 + (n - 1)d$ Step 4: Substitute the values to find the $20^{th$ term ($a_{20}$).}
Here, $n = 20$, $a_1 = 3$, and $d = 6$. $a_{20} = 3 + (20 - 1) \times 6$$a_{20} = 3 + (19) \times 6$$a_{20} = 3 + 114$$a_{20} = 117$ Therefore, the $20^{th}$ term of the series is 117.