Question

In a flower bed there are 23 rose plants in the first row, 21 in the second, 19 in the third and so on. There are 5 rose plants in the last row. Then the number of rows in the flower bed is:

• A. 5
• B. 10
• C. 15
• D. 20

Hint:

When you identify a sequence as an arithmetic progression, clearly list the values of the first term (\(a_1\)), the last term (\(a_n\)), and the common difference (d) before plugging them into the formula. This minimizes errors.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The number of plants in the rows forms an arithmetic progression (AP), as the difference between consecutive terms is constant.
Step 2: Key Formula or Approach:
The formula for the nth term of an AP is:
\(a_n = a_1 + (n-1)d\)
where \(a_n\) is the nth term, \(a_1\) is the first term, n is the number of terms, and d is the common difference.
We need to find 'n' (the number of rows).
Step 3: Detailed Explanation:
The sequence of the number of plants is 23, 21, 19, ... , 5.
The first term, \(a_1 = 23\).
The last term, \(a_n = 5\).
The common difference, \(d = 21 - 23 = -2\).
Now, substitute these values into the nth term formula:
\(5 = 23 + (n-1)(-2)\)
Subtract 23 from both sides:
\(5 - 23 = (n-1)(-2)\)
\(-18 = (n-1)(-2)\)
Divide both sides by -2:
\(\frac{-18}{-2} = n-1\)
\(9 = n-1\)
Add 1 to both sides:
\(n = 10\)
Step 4: Final Answer:
There are 10 rows in the flower bed.