NCERT Class 10 Maths — Chapter 5

Exercise 5.2: nth Term of an AP

The big exercise. Use aₙ = a + (n-1)d to find any term, check if a number belongs to an AP, and solve word problems. Lots of practice here.

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These questions cover the same concepts as Exercise 5.2. Try solving them to build confidence before or after the textbook exercise.

If the sum of the first 'n' terms of an AP is given by S_n = 3n² + 5n, what is the common difference of the AP?

A.3

B.5

C.6

D.8

For an AP, if the first term is 'a' and the common difference is 'd', which of the following statements is INCORRECT?

A.The n-th term is given by a_n = a + (n-1)d

B.The common difference 'd' can be zero.

C.The terms of an AP always increase if 'd' is positive.

D.If a sequence has a constant difference between consecutive terms, it is an AP.

If the sum of the first n terms of an Arithmetic Progression is given by S_n = Pn + Qn², where P and Q are constants, then the common difference of the AP is:

A.P + Q

B.P - Q

C.2Q

D.2P

A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2.5 m apart, what is the total length of wood required for the rungs?

A.3.85 m

B.4.25 m

C.4.5 m

D.5.2 m

If 2x + 1, x + 3, and 5 are consecutive terms of an AP, what is the value of x?

A.1

B.2

C.3

D.4

If the common difference of an AP is 5, what is the value of a_18 - a_13?

A.5

B.25

C.15

D.30

Which of the following sequences is an Arithmetic Progression (AP)?

A.2, 4, 8, 16, ...

B.1, 4, 9, 16, ...

C.3, 6, 9, 12, ...

D.1/2, 1/3, 1/4, 1/5, ...

A student wrote the first few terms of an AP as 5, 8, 11, 14, ... and concluded that the 10th term is 32. Identify the mistake in their reasoning.

A.The first term 'a' is incorrectly identified.

B.The common difference 'd' is incorrectly calculated.

C.The formula for the n-th term was applied incorrectly.

D.There is no mistake; the 10th term is indeed 32.

The sum of the first `n` terms of an AP is given by `Sn = 3n^2 + 5n`. What is the common difference of this AP?

A.3

B.5

C.6

D.8

A sum of money is divided among 10 prizes to be given to students for their overall academic performance. If each prize after the first is ₹20 less than its preceding prize, and the total sum of prizes is ₹1600, what is the value of the first prize?

A.₹250

B.₹280

C.₹300

D.₹320

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