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AP Board Class 10 Maths Chapter 6 Progressions Ex 6.5 Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 6 Progressions Ex 6.5 Book Answers

 AP Board Class 10 Maths Chapter 6 Progressions Ex 6.5 Textbook Solutions PDF: Download Andhra Pradesh Board STD 10th Maths Chapter 6 Progressions Ex 6.5 Book Answers

Andhra Pradesh State Board Class 10th Maths Chapter 6 Progressions Ex 6.5 Books Solutions

 Board AP Board Materials Textbook Solutions/Guide Format DOC/PDF Class 10th Subject Maths Chapters Maths Chapter 6 Progressions Ex 6.5 Provider Hsslive

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Find below the list of all AP Board Class 10th Maths Chapter 6 Progressions Ex 6.5 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:

10th Class Maths 6th Lesson Progressions Ex 6.5 Textbook Questions and Answers

Question 1.
For each geometric progression find the common ratio ‘r’, and then find an.
i) 3, 32, 34, 38, …….
Given G.P.: 3, 32, 34, 38, …….

ii) 2, -6, 18, -54, …….
Given G.P. = 2, -6, 18, -54, …….
a = 2, r = 𝑎2𝑎1 = −62 = -3
an = a . rn-1 = 2 × (-3)n-1
∴ r = -3; an = 2(-3)n-1

iii) -1, -3, -9, -27, ……
Given G.P. = -1, -3, -9, -27, ……
a = -1, r = 𝑎2𝑎1 = −3−1 = 3
an = a . rn-1 = (-1) × 3n-1
∴ r = 3; an = (-1) × 3n-1

iv) 5, 2, 45, 825, …….
Given G.P. = 5, 2, 45, 825, …….
a = 5, r = 𝑎2𝑎1 = 25
an = a . rn-1 = 5 × (25)𝑛−1
∴ r = 25; an = 5(25)𝑛−1

Question 2.
Find the 10th and nth term of G.P.: 5, 25, 125,…..
Given G.P.: 5, 25, 125,…..
a = 5, r = 𝑎2𝑎1 = 255 = 5
an = a . rn-1 = 5 × (5)n-1 = 51+n-1 = 5n
a10 = a . r9 = 5 × 59 = 510
∴ a10 = 510; an = 5n

Question 3.
Find the indicated term of each geometric progression.
i) a1 = 9; r = 13; find a7.
an = a . rn-1

ii) a1 = -12; r = 13; find a6.
an = a . rn-1

Question 4.
Which term of the G.P.
i) 2, 8, 32,….. is 512?
Given G.P.: 2, 8, 32,….. is 512
a = 2, r = 𝑎2𝑎1 = 82 = 4
Let the nth term of G.P. be 512

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 29
∴ 2n – 1 = 9
[∵ bases are equal, exponents are also equal]
∴ 2n = 9 + 1 = 10
n = 102 = 5
∴ 512 is the 5th term of the given G.P.

ii) √3, 3, 3√3, …….. is 729?
Given G.P.: √3, 3, 3√3, …….. is 729
a = √3, r = 𝑎2𝑎1 = 33√ = √3
now an = a . rn-1 = 729
⇒ (√3)(√3)n-1 = 729
⇒ (√3)n = 36 = (√3)12
⇒ n = 12
So 12th term of GP √3, 3, 3√3, …….. is 729.

iii) 13, 19, 127, ……. is 12187?
Given G.P.: 13, 19, 127, ……. is 12187

Let 12187 be the nth term of the G.P., then
an = a . rn-1 = 12187

[∵ bases are equal, exponents are also equal]
7th term of G.P is 12187.

Question 5.
Find the 12th term of a G.P. whose 8 term is 192 and the common ratio is 2.
Given a G.P. such that a8 = 192 and r = 2
an = a . rn-1
a8 = a . (2)8-1 = 192

= 3 × 210 = 3 × 1024 = 3072.

Question 6.
The 4th term of a geometric progression is 23 and the seventh term is 1681. Find the geometric series.
Given: In a G.P.

Now substituting r = 23 in equation (1)
we get,

Question 7.
If the geometric progressions 162, 54, 18, ….. and 281, 227, 29,….. have their nth term equal, find the value of n.
Given G.P.: 162, 54, 18, ….. and 281, 227, 29,……

Given that nth terms are equal
an = a . rn-1

⇒ 3n-1+n-1 = 81 × 81
⇒ 32n-2 = 34 × 34
⇒ 32n-2 = 38 [∵ am . an = am+n]
⇒ 2n – 2 = 8
[∵ bases are equal, exponents are also equal]
2n = 8 + 2
⇒ n = 102 = 5
The 5th terms of the two G.P.s are equal.

Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Ex 6.5 Textbooks for Exam Preparations

Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Ex 6.5 Textbook Solutions can be of great help in your Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Ex 6.5 exam preparation. The AP Board STD 10th Maths Chapter 6 Progressions Ex 6.5 Textbooks study material, used with the English medium textbooks, can help you complete the entire Class 10th Maths Chapter 6 Progressions Ex 6.5 Books State Board syllabus with maximum efficiency.

FAQs Regarding Andhra Pradesh Board Class 10th Maths Chapter 6 Progressions Ex 6.5 Textbook Solutions

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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