Question

Which term of the series 545, 525, 505, 485.... is closest to zero?

• A. 30
• B. 29
• C. 28
• D. 37
• E. None of these

Answer 1

The Correct Option is C

Step 1: Analyze the given series.
The given series is: 545, 525, 505, 485, ...
The series is decreasing, and we can see that the common difference between consecutive terms is:
525 - 545 = -20
505 - 525 = -20
485 - 505 = -20
Hence, the common difference \( d = -20 \).

Step 2: Use the formula for the nth term of an arithmetic progression.
The nth term of an arithmetic progression is given by the formula:
\( T_n = a + (n-1) \times d \)
where:
- \( T_n \) is the nth term,
- \( a \) is the first term (545),
- \( d \) is the common difference (-20),
- \( n \) is the term number.
We need to find the term closest to zero, so we set \( T_n = 0 \).

Step 3: Set up the equation for the nth term.
Set \( T_n = 0 \) and solve for \( n \):
\( 0 = 545 + (n-1) \times (-20) \)
\( 0 = 545 - 20(n-1) \)
\( 20(n-1) = 545 \)
\( n-1 = \frac{545}{20} = 27.25 \)
\( n = 27.25 + 1 = 28.25 \)

Step 4: Determine the closest integer.
Since the term number must be an integer, the 28th term will be closest to zero. Hence, the 28th term is closest to zero.

Final Answer:
The correct option is (C): 28.