Question 452 marksShort AnswerSection E

What is the total distance the competitor has to run ?

Arithmetic Progressions
Arithmetic Progressions - Sum of n terms (Potato Race)

Official answer

The round-trip distances 10,16,22,…10, 16, 22, \ldots form an AP with a=10 ma = 10\text{ m} and d=6 md = 6\text{ m} for n = 10 potatoes. Applying Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a + (n - 1)d], S10=5[20+9(6)]=5×74=370 mS_{10} = 5[20 + 9(6)] = 5 \times 74 = 370\text{ m}. Hence the competitor runs a total distance of 370 m.

Answer keywords:sum of AParithmetic progressiontotal distancepotato raceSn formula10 potatoes

Marking scheme

  1. 1.1 mark: correctly identifying a=10,d=6,n=10a = 10, d = 6, n = 10 and writing the sum formula Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a+(n-1)d].
  2. 2.1 mark: correct substitution and final answer of 370 m.

Hint

Use Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a + (n-1)d] with a=10,d=6,n=10a = 10, d = 6, n = 10.

Quick oral answer

The round-trip distances form an AP with a=10 m,d=6 m,n=10a = 10\text{ m}, d = 6\text{ m}, n = 10; using Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a+(n-1)d], the total distance is 370 m.

Common mistakes

  1. 1.Using d=3 md = 3\text{ m} (the one-way gap) instead of d=6 md = 6\text{ m} (the round-trip increase).
  2. 2.Arithmetic slip in (n−1)d(n-1)d, e.g. using n instead of (n − 1).
  3. 3.Manually adding ten terms and making an addition error instead of using the sum formula.

Analysis and explanation

The culminating step of the case study: modelling the ten round-trip distances as an AP and summing them.


Concept

  • Round-trip distances 10,16,22,…10, 16, 22, \ldots form an AP with a=10 ma = 10\text{ m} (Q43) and d=6 md = 6\text{ m} (from Q43 to Q44).
  • Total distance for 10 potatoes = Sₙ using the standard AP sum formula.

Key Points

  • Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a + (n - 1)d], with n=10,a=10,d=6n = 10, a = 10, d = 6.
  • S10=5[20+54]=370 mS_{10} = 5[20 + 54] = 370\text{ m}.

Common Mistakes

  • Using (n−1)=10(n - 1) = 10 instead of 9 inside the formula.
  • Taking d=3 md = 3\text{ m} (the one-way gap) instead of the correct round-trip value d=6 md = 6\text{ m}.

Real-World

  • Shows how AP models practical sports-event logistics like relay/potato races.

Interesting facts

This exact potato-race scenario (bucket 5 m away, potatoes 3 m apart, 10 potatoes) is one of the most quoted real-life applications of Arithmetic Progressions in NCERT Class 10 Mathematics.

The total distance of 370 m is roughly equivalent to running almost one full lap of a standard 400 m athletics track.

Question details

Q45 of 56 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Standard)
Year
2026
Section
Section E
Marks
2
Type
Short Answer
Chapter
Arithmetic Progressions
Topic
Arithmetic Progressions - Sum of n terms (Potato Race)
Bloom's level
apply
Syllabus topic
Unit II: Algebra — Arithmetic Progressions: Sum of first n terms of an AP
Author
CBSE
Reviewed by
Padhantu Academic Team

Spotted a mistake or something unclear?

Tell us and we will fix it.

Frequently asked questions

Why is the common difference 6 m and not 3 m?

Because the 3 m gap between consecutive potatoes affects both the outward and return trip, doubling to a 6 m increase in round-trip distance for each successive potato.

Can this be solved without the AP sum formula?

Yes, by manually adding all ten round-trip distances (10+16+22+…+6410+16+22+\ldots+64), but using Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a+(n-1)d] is faster and less error-prone.