Question

The missing term (?) of the Arithmetic Progression (AP) 3, 2, 33, 48, 33, 48. ….is

• A. 18
• B. 16
• C. 20
• D. 22

Answer 1

The Correct Option is A

Step 1: Recall the formula for the \( n \)-th term of an AP.

The \( n \)-th term of an AP is given by:

\[ a_n = a + (n - 1)d, \]

where \( a \) is the first term and \( d \) is the common difference.

Step 2: Identify known terms and find the common difference \( d \).

The first term \( a = 3 \). The third term is \( a_3 = 33 \), and the fourth term is \( a_4 = 48 \).

Using the formula for the \( n \)-th term:

\[ a_3 = a + 2d \quad \text{and} \quad a_4 = a + 3d. \]

Substitute \( a_3 = 33 \) and \( a = 3 \):

\[ 33 = 3 + 2d \implies 2d = 30 \implies d = 15. \]

Step 3: Find the second term (\( a_2 \)).

The second term is given by:

\[ a_2 = a + d = 3 + 15 = 18. \]

Final Answer: The missing term is \( \mathbf{18} \).