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AP Board Class 10 Maths Chapter 6 Progressions Optional Exercise Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 6 Progressions Optional Exercise Book Answers

AP Board Class 10 Maths Chapter 6 Progressions Optional Exercise Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 6 Progressions Optional Exercise Book Answers
AP Board Class 10 Maths Chapter 6 Progressions Optional Exercise Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 6 Progressions Optional Exercise Book Answers


AP Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbooks Solutions and answers for students are now available in pdf format. Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Optional Exercise Book answers and solutions are one of the most important study materials for any student. The Andhra Pradesh State Board Class 10th Maths Chapter 6 Progressions Optional Exercise books are published by the Andhra Pradesh Board Publishers. These Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Optional Exercise textbooks are prepared by a group of expert faculty members. Students can download these AP Board STD 10th Maths Chapter 6 Progressions Optional Exercise book solutions pdf online from this page.

Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbooks Solutions PDF

Andhra Pradesh State Board STD 10th Maths Chapter 6 Progressions Optional Exercise Books Solutions with Answers are prepared and published by the Andhra Pradesh Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of AP Board Class 10th Maths Chapter 6 Progressions Optional Exercise Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 10th Maths Chapter 6 Progressions Optional Exercise solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Andhra Pradesh Board STD 10th Maths Chapter 6 Progressions Optional Exercise Textbooks. These Andhra Pradesh State Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Andhra Pradesh Board.

Andhra Pradesh State Board Class 10th Maths Chapter 6 Progressions Optional Exercise Books Solutions

Board AP Board
Materials Textbook Solutions/Guide
Format DOC/PDF
Class 10th
Subject Maths
Chapters Maths Chapter 6 Progressions Optional Exercise
Provider Hsslive


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AP Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

10th Class Maths 6th Lesson Progressions Optional Exercise Textbook Questions and Answers

Question 1.
Which term of the AP:
121, 117, 113,…, is the first negative term? [Hint: Find n for an < 0]
Answer:
Given A.P: 121, 117, 113, ……
a = 121 and d = a2 – a1
= 117 – 121 = -4
Let the nth term be the first negative term of the given G.P.
Then, an < 0
⇒ an = a + (n – 1) d < 0
⇒ 121 + (n – 1) (-4) < 0
⇒ 121 – 4n + 4 < 0
⇒ 125 – 4n < 0
⇒ -4n < -125
⇒ 4n >125 125
⇒ n > 1254
n > 31.25
∴ When n = 32, the term becomes negative, (or)
32 nd term is the first negative term of the given A.P.

Question 2.
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Answer:
Let the 3rd term of AP = a + 2d
and the 7th term of AP = a + 6d
∴ Sum of 3rd and 7th terms = a + 2d + a + 6d = 6
⇒ 2a + 8d = 6
⇒ a + 4d = 3 …… (1)
Now product of above two terms = (a + 2d) (a + 6d) = 8
we can re-write above terms as following
(a + 4d – 2d) (a + 4d + 2d) = 8
⇒ (3 – 2d) (3 + 2d) = 8
⇒ 9 – 4d2 = 8
⇒ 4d2 = 9 – 8 = 1
∴ d2 = 14
⇒ d = ± 12 ……. (2)
Now putting d = 12 in eq(1) we get
a + 4d = a + 4(12) = 3 ⇒ a = 1
so a = 1, d = 12
(or) now putting d = −12, we get
a + 4d = a + 4(−12) = 3
⇒ a – 2 = 3
⇒ a = 5
∴ a = 5, d = −12
∴ Sum of sixteen terms =

So S16 = 20 or 76

Question 3.
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 the bottom rungs are 212 m apart, what is the length of the wood required for the rungs. [Hint: Number of rungs = 25025 + 1]

Answer:
Given: A ladder with rungs separated by a distance of 25 cm.
Total distance between the rungs = 212 m = 250 m
∴ Number of rungs = 25025 + 1 = 10 + 1 = 11
Length of the bottom and top rungs = 45 cm and 25 cm
where a = 45; last term l = a11 = 25 and d = 2 cm
∴ Sn = 𝑛2(a + l)
= 112(45 + 25)
= 112 × 70
= 35 × 11
= 385 cm
∴ Length of wood required for total rungs = 385 cm.

Question 4.
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. And find this value of x. [Hint: Sx-1 = S49 – Sx]
Answer:
Given: Houses with numbers from 1 to 49.
x is a number x such that,
Sx-1 = S49 – Sx


⇒ x(x – 1) + x(x + 1) = 2 × 1225
⇒ x2 – x + x2 + x = 2450
⇒ 2x2 = 2450
⇒ x2 = 24502 = 1225
⇒ x = √1225 = ±35
∴ x = 35 [∵ x is a counting number]

Question 5.
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete.
Each step has a rise of 14 m and a tread of 12 m. (see Fig.).
Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = 14 × 12 × 50 m ]

Answer:
Length of each step = 50 m = l
Rise/height of each step = 14 m = h
Tread of each step = 12 m = b
Given volume of concrete required to build the first step = 14 × 12 × 50 m3 = lbh
We can compare the shape of each step with a cuboid.
Volume of the cuboid = l . b . h
Volumes of concrete required to build the 15 steps are

[∵ 1, 2, 3, 15 is in A.P. where a = 1; d = 1, n = 15]

∴ The total volume of concrete required to build the terrace is 750 m3.

Question 6.
150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped from the work in the second day. Four workers dropped in third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.
[Let the no.of days to finish the work is ‘x’ then 150x = 𝑥+82[2 × 150 + (x + 8 – 1) (-4)]
Answer:
Given: Number of workers engaged initially = 150.
4 workers were dropped each day.
Let the total work was to be completed initially was in x days.
∴ Work done by 150 workers in x days = 150.x.
But due to the dropping of 4 workers each day it took 8 more days.
Work done in this case is
150 × 1 + 146 × 1 + 142 × 1 + …. (x + 8) terms,

= (x + 8) (136 – 2x)
= -2x2 + 136x + 1088 – 16x
= -2x2 + 120x + 1088
∴ 150x = -2x2 + 120x + 1088
⇒ 2x2 + 30x – 1088 = 0
⇒ x2 + 15x – 544 = 0
⇒ x2 + 32x – 17x – 544 =0
⇒ x(x + 32) – 17 (x + 32) = 0
⇒ (x + 32) (x – 17) = 0
⇒ x + 32 = 0 (or) x – 17 = 0
⇒ x = – 32 (or) x = 17
x can’t be negative.
∴ x = 17.
i.e., The total work was completed in x + 8 days = 17 + 8 = 25 days.

Question 7.
A machine costs Rs. 5,00,000. If the value depreciates 15% in the first year, 1312% in the second year, 12% in the third year and so on. What will be its value at the end of 10 years, when all the percentages will be applied to the original cost?
Answer:
Given: Cost price of a machine = Rs. 5,00,000
Depreciation during the years

Sum of the depreciations =

∴ Cost after 10 years = (100 – 82.5)% of 5,00,000
= 17.5 % of 5,00,000
= 17.5×5000002
= Rs. 87,500
∴ The value at the end of 10 years will be Rs. 87,500.


AP Board Textbook Solutions PDF for Class 10th Maths


Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbooks for Exam Preparations

Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbook Solutions can be of great help in your Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Optional Exercise exam preparation. The AP Board STD 10th Maths Chapter 6 Progressions Optional Exercise Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 6 Progressions Optional Exercise Books State Board syllabus with maximum efficiency.

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How to get AP Board Class 10th Maths Chapter 6 Progressions Optional Exercise Textbook Answers??

Students can download the Andhra Pradesh Board Class 10 Maths Chapter 6 Progressions Optional Exercise Answers PDF from the links provided above.

Can we get a Andhra Pradesh State Board Book PDF for all Classes?

Yes you can get Andhra Pradesh Board Text Book PDF for all classes using the links provided in the above article.

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