# NCERT Class 10 Mathematics Chapter 5 Arithmetic Progressions Solutions: In-Text and Exercise Questions Explained | SwaVid

An Arithmetic Progression (AP) is a sequence of numbers such that the difference between consecutive terms is constant. This constant difference is call...

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# Arithmetic Progressions

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Chapter 5 · Class 10 Mathematics

An Arithmetic Progression (AP) is a sequence of numbers such that the difference between consecutive terms is constant. This constant difference is called the common difference, denoted by 'd'. The first term of an AP is usually denoted by 'a'. The general form of an AP is a, a + d, a + 2d, a + 3d, ... The nth term of an AP is given by the formula a_n = a + (n-1)d. The sum of the first n terms of an AP is given by S_n = n/2 [2a + (n-1)d] or S_n = n/2 [a + l], where 'l' is the last term. This chapter explores identifying APs, finding their terms, and calculating their sums.

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Exercise 5.1

Answer: Yes, the list of numbers forms an Arithmetic Progression because the common difference between consecutive terms is constant (₹ 8).

Exercise 5.2

Exercise 5.3

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- Let the taxi fare for the first km be a_1.
- a_1 = ₹ 15.
- The fare for the first 2 km will be the fare for the first km plus the fare for the additional km: a_2 = 15 + 8 = ₹ 23.
- The fare for the first 3 km will be the fare for the first 2 km plus the fare for the additional km: a_3 = 23 + 8 = ₹ 31.
- The fare for the first 4 km will be the fare for the first 3 km plus the fare for the additional km: a_4 = 31 + 8 = ₹ 39.
- The list of fares is 15, 23, 31, 39, ...
- To check if it's an AP, find the difference between consecutive terms:
- d_1 = a_2 - a_1 = 23 - 15 = 8.
- d_2 = a_3 - a_2 = 31 - 23 = 8.
- d_3 = a_4 - a_3 = 39 - 31 = 8.
- Since the difference between consecutive terms is constant (d = 8), the list of numbers forms an Arithmetic Progression.
- NCERT Class 10 Mathematics textbook: Mathematics : Chapter 5: Arithmetic Progressions

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