NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.4 are provided to help students prepare effectively for their Class 10 board exams. These solutions are created by subject experts and strictly follow the latest CBSE syllabus and guidelines.
Exercise 5.4 mainly focuses on finding the sum of the first n terms of an Arithmetic Progression (AP). Students learn how to apply the standard formula to calculate the sum when the first term, common difference, and number of terms are given.
NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.4
Q.
Which term of the AP: 3, 8, 13, 18, . . . , is 78?
Q.
Which term of the AP: 3, 15, 27, 39, . . . will be 132 more than its 54th term?
Q.
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Q.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in the following figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take π =22/7)
[Hint: Length of successive semicircles is
l1,
l2,
l3,
l4, . . . with centres at A, B, A, B, . . ., respectively.]
Q.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line(see the following figure)
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: To pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 × (5 + 3)]
Q.
Q.
Which term of the AP 3, 15, 27, 39, … will be 120 more than its 21st term?
[CBSE - 2019]
NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.4
The key formula used in this exercise is:
Sn=2n[2a+(n−1)d]
By practicing this exercise, students gain clarity in:
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Calculating the sum of n terms
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Using the nth term and sum formula together
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Solving application-based problems
The solutions are explained in a step-by-step and easy-to-understand manner, making revision simple and effective.
FAQs: Class 10 Maths Chapter 5 – Arithmetic Progressions Exercise 5.4
Q1. What is the focus of Exercise 5.4?
Answer:
Exercise 5.4 focuses on finding the sum of the first n terms of an Arithmetic Progression using the standard formula.
Q2. What is the formula for the sum of n terms in an AP?
Answer:
The sum of the first n terms is given by:
Sn=2n[2a+(n−1)d]
where:
-
a = first term
-
d = common difference
-
n = number of terms
Q3. Is there another formula to find the sum of n terms?
Answer:
Yes. If the nth term
an is known, the formula is:
Sn=2n(a+an)
Q4. How do I solve sum-based word problems in AP?
Answer:
-
Identify the first term
a, common difference
d, and number of terms
n.
-
Use the appropriate sum formula.
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Substitute the values and simplify carefully.
Q5. How do NCERT Solutions help in board exams?
Answer:
These solutions provide clear, step-by-step explanations, helping students apply formulas correctly and avoid common mistakes. Regular practice improves speed and accuracy in exams.