The correct answer is option (C):
28
Let's analyze the given series: 545, 525, 505, 485...
First, we need to determine the type of series. We can look at the difference between consecutive terms:
525 - 545 = -20
505 - 525 = -20
485 - 505 = -20
Since the difference between consecutive terms is constant, this is an arithmetic series with a common difference (d) of -20.
The first term (a1) of the series is 545.
The formula for the nth term (an) of an arithmetic series is:
an = a1 + (n-1)d
We want to find the term that is closest to zero. This means we are looking for a value of 'n' such that 'an' is as close to 0 as possible.
Let's set the nth term equal to 0 and solve for 'n' to get an idea of where zero would fall in the series:
0 = 545 + (n-1)(-20)
0 = 545 - 20n + 20
0 = 565 - 20n
20n = 565
n = 565 / 20
n = 28.25
Since 'n' must be a whole number (representing the term number), the term closest to zero will be either the 28th term or the 29th term. We need to calculate both of these terms and see which one is closer to zero.
Calculate the 28th term (a28):
a28 = a1 + (28-1)d
a28 = 545 + (27)(-20)
a28 = 545 - 540
a28 = 5
Calculate the 29th term (a29):
a29 = a1 + (29-1)d
a29 = 545 + (28)(-20)
a29 = 545 - 560
a29 = -15
Now, let's compare the absolute values of these terms to zero:
The absolute value of the 28th term is |5| = 5.
The absolute value of the 29th term is |-15| = 15.
Comparing 5 and 15, the value 5 is closer to zero.
Therefore, the 28th term of the series is closest to zero.
The final answer is $\boxed{28}$.