- A160 m
- B320 m
- C288 m
- D68 m
Step-by-Step Solution
Distances to the potatoes are 6, 10, 14, …, 34 m. Each trip is there and back: m.
Answer: B) 320 m
In a potato race at a school sports day, a bucket is placed at the start. The first potato is 6 m from the bucket and the 8 potatoes are 4 m apart in a straight line. A runner fetches one potato at a time and drops it in the bucket. What total distance does she run?
Class 10Arithmetic ProgressionsAlgebra — Sequences
Key idea: Sum of first n terms
**Sₙ = []**
Or equivalently, **Sₙ = **, where is the LAST term (the n-th term).
**Why these are equal**: , so .
**Example**: Sum of 1, 4, 7, …, 28.
First find . From aₙ = 28: → .
Then S₁₀ = .
**Special case natural numbers)**: Sₙ = .
**First odd numbers**: Sₙ = .
**First even numbers**: Sₙ = .
Or equivalently, **Sₙ = **, where is the LAST term (the n-th term).
**Why these are equal**: , so .
**Example**: Sum of 1, 4, 7, …, 28.
First find . From aₙ = 28: → .
Then S₁₀ = .
**Special case natural numbers)**: Sₙ = .
**First odd numbers**: Sₙ = .
**First even numbers**: Sₙ = .
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