NCERT Class 10 Maths — Chapter 5

Exercise 5.1: Introduction to AP

Identify which sequences form an AP, find common differences, and recognise APs in everyday situations.

identifying APcommon differenceAP from real life

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Extra Practice Questions

These questions cover the same concepts as Exercise 5.1. Try solving them to build confidence before or after the textbook exercise.

Which of the following represents an arithmetic progression where the terms are decreasing?

A.a = 7, d = 3

B.a = -2, d = 5

C.a = 10, d = -2

D.a = 0, d = 0

The sum of the first 'n' terms of an AP is given by S_n = 2n² + 3n. What is the 'n'th term, a_n?

A.4n + 1

B.4n + 5

C.2n² + 3n - 1

D.2n² + 3n

If (a² + b²), (b² + c²), and (c² + a²) are in an Arithmetic Progression, then which of the following statements must be true?

A.a, b, c are in AP

B.a², b², c² are in AP

C.a, c, b are in AP

D.b², a², c² are in AP

The sum of the first 15 multiples of 8 is:

A.900

B.920

C.960

D.1000

A sequence is defined by a_n = 5n - 2. What is the sum of the first term and the common difference of this sequence?

A.5

B.8

C.10

D.3

A person saves ₹100 in the first month, ₹150 in the second month, ₹200 in the third month, and so on. If their savings form an AP, what does the common difference 'd' represent in this context?

A.The total amount saved

B.The initial saving amount

C.The fixed increase in saving each month

D.The number of months for saving

A student claims that the sum of the first 'n' terms of an Arithmetic Progression is given by the formula Sn = n^2 + 5n - 2. Which of the following statements about this AP is true?

A.The common difference is 4.

B.The first term is 4.

C.The given formula cannot represent the sum of an AP.

D.The 10th term is 42.

If a, b, c are in an Arithmetic Progression, then which of the following sequences is *always* an Arithmetic Progression?

A.a², b², c²

B.a-k, b-k, c-k (for any constant k)

C.1/a, 1/b, 1/c

D.ab, bc, ca

If the ratio of the 11th term to the 18th term of an AP is 2:3, what is the ratio of its 5th term to its 21st term?

A.1/3

B.2/3

C.1/4

D.2/5

A spiral is made up of successive semicircles, with centers alternately at A and B, starting with center A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... What is the total length of such a spiral made up of 13 consecutive semicircles? (Use π = 22/7).

A.143 cm

B.77 cm

C.286 cm

D.110 cm

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