NCERT Class 10 Maths — Chapter 5

Exercise 5.3: Sum of n Terms of an AP

Another big exercise. Calculate the sum of first n terms, find how many terms are needed for a given sum, and tackle word problems about savings, distances, and more.

sum formulaSₙ = n/2[2a + (n-1)d]finding n given sum
20
NCERT Questions
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Practice MCQs
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Key Concepts
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Extra Practice Questions

These questions cover the same concepts as Exercise 5.3. Try solving them to build confidence before or after the textbook exercise.

1

The sum of the first 15 multiples of 8 is:

A.900
B.920
C.960
D.1000
2

A gardener plants 15 saplings on the first day, 18 on the second day, 21 on the third day, and so on. If this pattern continues, how many saplings will he plant on the 7th day?

A.27
B.30
C.33
D.36
3

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

A.1, 3, 6, 10, ...
B.2, 4, 8, 16, ...
C.3, 6, 9, 12, ...
D.1/2, 1/3, 1/4, 1/5, ...
4

A man saves ₹1000 in the first month, ₹1200 in the second month, ₹1400 in the third month, and so on. If he wants to save a total of ₹1,00,000, in how many months will he achieve this?

A.20
B.25
C.30
D.35
5

If the sum of the first m terms of an AP is equal to the sum of the first n terms (where m ≠ n), then the sum of its first (m + n) terms is:

A.a
B.d
C.0
D.m+n
6

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
7

A student saves ₹5 on the first day, ₹10 on the second day, ₹15 on the third day, and so on. If this pattern continues, what will be her savings on the 20th day?

A.₹95
B.₹100
C.₹105
D.₹110
8

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

A.1:2
B.1:3
C.2:5
D.3:7
9

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
10

If a1, a2, a3, ..., an are in an Arithmetic Progression with common difference 'd', then the sum of the series 1/(a1×a2) + 1/(a2×a3) + ... + 1/(a(n-1)×an) is:

A.1/(a1 - an)
B.(n-1) / (a1 × an)
C.n / (a1 × an)
D.d / (a1 × an)

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Common Mistakes to Avoid

  • Confusing the two sum formulas: Sₙ = n/2[2a + (n-1)d] and Sₙ = n/2[a + l]
  • Not finding n first when both a and l are known
  • Forgetting that Sₙ - Sₙ₋₁ gives the nth term

Other Exercises in Chapter 5

Frequently Asked Questions

How many questions are in Exercise 5.3?

Exercise 5.3 has 20 questions on finding sums of APs, a mix of direct computation and word problems.

What is the formula for sum of AP?

Sₙ = n/2 × [2a + (n-1)d] or equivalently Sₙ = n/2 × (a + l) where l is the last term.

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