Question

In each of the following questions a number series is given with one missing (?) term. The term is given as one of the alternatives among the five numbers given in the answer choic Find the term.
81, 9, 64, 8, 49,?

• A. 10
• B. 7
• C. 5
• D. 4
• E. 36

Answer 1

The Correct Option is B

Step 1: Analyze the pattern of the given series.
The given series is: 81, 9, 64, 8, 49, ?
Let's break it down: - 81 is a perfect square: \( 81 = 9^2 \) - 9 is a perfect square: \( 9 = 3^2 \) - 64 is a perfect square: \( 64 = 8^2 \) - 8 is a cube: \( 8 = 2^3 \) - 49 is a perfect square: \( 49 = 7^2 \)

Step 2: Identify the pattern.
The numbers alternate between perfect squares and cubes: - 81 (square of 9) - 9 (square of 3) - 64 (square of 8) - 8 (cube of 2) - 49 (square of 7)
Therefore, the next term should be the cube of 1, which is 1.

Step 3: Correct the pattern.
It seems the last term we are looking for should continue the alternating pattern, so after 49 (which is the square of 7), the next number should be the square of 7, resulting in the answer: 7.

Final Answer:
The missing term in the series is 7.