Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.
Arithmetic Progressions
EXAMPLES
CBSE_NCERT_TEXTBOOK
Grade 10
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. How many rows are there in the flower bed?
Step-by-Step Solution
Key Concept: The numbers of rose plants form an Arithmetic Progression (AP) with first term \(a_1 = 23\) and common difference \(d = -2\). Use the nth‑term formula \(a_n = a_1 + (n-1)d\) to find the total number of rows \(n\).
1. Identify the AP: - First term \(a_1 = 23\). - Second term \(21\) ⇒ common difference \(d = 21-23 = -2\). 2. The last term given is \(a_n = 5\). 3. Use the nth‑term formula of an AP: $$a_n = a_1 + (n-1)d$$ Substitute the known values: $$5 = 23 + (n-1)(-2)$$ 4. Solve for \(n\): $$5 - 23 = (n-1)(-2)$$ $$-18 = -2(n-1)$$ $$n-1 = \frac{-18}{-2} = 9$$ $$n = 9 + 1 = 10$$ 5. Hence, the flower bed contains 10 rows of rose plants.
Correct Answer:10 rows
Mathbee AI Mentor (Free Demo)
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.
Master Arithmetic Progressions with Mathbee
Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.