Question

An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the position and nature of the image.

• A. \(20\) cm in front, real and inverted
• B. \(30\) cm in front, real and inverted
• C. \(30\) cm behind, virtual and erect
• D. \(15\) cm behind, virtual and erect

Hint:

Always apply the Cartesian sign convention in mirror problems: distances measured in front of the mirror are negative, and distances behind the mirror are positive.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given a sequence of numbers and need to identify the underlying mathematical rule to find the next term.
Step 2: Key Formula or Approach:
The first step in series completion is to check the difference between consecutive terms. If the difference is not constant, check if the differences themselves form a sequence.
Step 3: Detailed Explanation:
Let's analyze the gaps between the terms:
\( 6 - 2 = 4 \)
\( 12 - 6 = 6 \)
\( 20 - 12 = 8 \)
\( 30 - 20 = 10 \)
The differences are \( 4, 6, 8, 10 \).
We see that the difference is increasing by \( 2 \) at each step.
The next difference should be \( 10 + 2 = 12 \).
Therefore, the missing number is \( 30 + 12 = 42 \).
Alternatively, the pattern can be seen as \( n^2 + n \):
\( 1^2 + 1 = 2 \)
\( 2^2 + 2 = 6 \)
\( 3^2 + 3 = 12 \)
\( 4^2 + 4 = 20 \)
\( 5^2 + 5 = 30 \)
\( 6^2 + 6 = 42 \).
Step 4: Final Answer:
The next number in the series is \( 42 \).