Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Ex 2.8

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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Ex 2.8

10th Maths Exercise 2.8 Question 1.
Find the sum of first n terms of the G.P.
(i) 5, -3, \(\frac { 9 }{ 5 } \), – \(\frac { 27 }{ 25 } \), ……….
(ii) 256, 64, 16, ……..
Solution:
(i) 5, -3, \(\frac { 9 }{ 5 } \), \(\frac { -27 }{ 25 } \), ………
10th Maths Exercise 2.8 Samacheer Kalvi
(ii) 256, 64, 16,…….
a = 256
Exercise 2.8 Class 10 Maths Solution Samacheer Kalvi

Exercise 2.8 Class 10 Maths Solution Question 2.
Find the sum of first six terms of the G.P. 5, 15, 45, …
Solution:
G.P.= 5, 15, 45, 15
Ex 2.8 Class 10 Samacheer Samacheer Kalvi

Ex 2.8 Class 10 Samacheer Question 3.
Find the first term of the GP. whose common ratio 5 and whose sum to first 6 terms is 46872.
Solution:
Common ratio, r = 5
S6 = 46872
10th Maths Exercise 2.8 Samacheer Kalvi

10th Maths Exercise 2.8 Samacheer Kalvi Question 4.
Find the sum to infinity of (i) 9 + 3 + 1 + ….
(ii) 21 + 14 + \(\frac { 28 }{ 3 } \) + ….
Solution:
(i) 9 + 3 + 1 + ….
10th Maths Exercise 2.8 In Tamil Samacheer Kalvi
(ii) 21 + 14 + \(\frac { 28 }{ 3 } \) + ….
Class 10 Maths Exercise 2.8 Solutions Samacheer Kalvi

10th Maths Exercise 2.8 In Tamil Question 5.
If the first term of an infinite G.P. is 8 and its sum to infinity is \(\frac { 32 }{ 3 } \) then find the common ratio.
Solution:
a = 8
2.8 Exercise Class 10 Samacheer Kalvi

Class 10 Maths Exercise 2.8 Solutions Question 6.
Find the sum to n terms of the series
(i) 0.4 + 0.44 + 0.444 +…. to n terms
(ii) 3 + 33 + 333 + …. to n terms
Solution:
(i) 0.4 + 0.44 + 0.444 + … to n terms
= 4 (0.1 + 0.11 + 0.111 + … to n terms)
= \(\frac { 4 }{ 9 } \) (0.9 + 0.99 + 0.999 + … to n terms)
= \(\frac { 4 }{ 9 } \) (1 -0.1) + (1 – 0.01) +(1 – 0.001) + … n terms)
Exercise 2.8 Class 10 Maths Samacheer Kalvi

(ii) 3 + 33 + 333 + … to n terms.
= 3 (1 + 11 + 111 + …….. to n terms)
= \(\frac { 3 }{ 9 } \) (9 + 99 + 999 +… to n terms)
\(\frac { 1 }{ 3 } \) = [(10 – 1) + (100 – 1) + (1000 – 1) + … to n terms]
= \(\frac { 1 }{ 3 } \) [(10 + 100 + 1000 + .. ) + (-1)n]
Ex 2.8 Class 10 Maths Samacheer Kalvi

2.8 Exercise Class 10 Question 7.
Find the sum of the Geometric series
3 + 6 + 12 + …… + 1536.
Solution:
3 + 6 + 12 + …… + 1536
Here a = 3
Maths Exercise 2.8 Class 10 Samacheer Kalvi

Exercise 2.8 Class 10 Maths Question 8.
Kumar writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with the instruction that they continue the process similarly. Assuming that the process is unaltered and it costs ₹2 to mail one letter, find the amount spent on postage when 8th set of letters is mailed.
Maths 2.8 Class 10 Samacheer Kalvi
Solution:
Kumar (1) 2 × 4
Cost of posting 1st set of Letters.
Cost of posting 2nd set of letters
10th Maths Exercise 2.8 10th Sum Samacheer Kalvi
Amount spent
[a + ar + ar2 +… arn-1]
= 4 [2 + 2 × 4 + 2 × 42 ÷ + 2 × 47]
= 4 [Sn] Here n = 8, r = 4
It is a G.P
10 Class Math Exercise 2.8 Solution Pdf Samacheer Kalvi
∴ Cost of postage after posting 8th set of letters
= 4 × 43690 = ₹ 174760

Ex 2.8 Class 10 Maths Question 9.
Find the rational form of the number 0.\(\overline{123}\)
Solution:
Let x = 0.123123123 ………. ⇒ x = 0.\(\overline{123}\) …..(1)
Multiplying 1000 on both rides
1000 x = 123.123123… ⇒ 1000x = 123.\(\overline{123}\) …..(2)
(2) – (1) = 1000x – x 123.\(\overline{123}\) – 0.\(\overline{123}\).
⇒ 999 x = 123
⇒ x = \(\frac { 123 }{ 999 } \)
⇒ x = \(\frac { 41 }{ 333 } \) Rational number

Maths Exercise 2.8 Class 10 Question 10.
If Sn = (x + y)+(x2 + xy + y2) + (x3 + x2y + xy2 + y3) + …n terms then prove that (x – y)
10 Class Math Exercise 2.8 Solution Samacheer Kalvi
Solution:
Sn = (x + y) + (x2 + xy + y2) + (x3 + x2y + xy2 + y3) + …n terms
⇒ x. Sn = (x + y)x + (x2 + xy + y2)x + (x3 + x2y + xy2 + y3) x + ….
⇒ x. Sn = x2 +xy + x3 + x2y + y2x + x4 + x3y
+ x2 y2 + y3 x +…… ….(1)
Multiplying ‘y’ on both sides,
= y.Sn = (x + y)y + (x2 + xy + y2) y+
(x3 + x2y + xy2 + y3) y + ….
= y.Sn = xy + y2 + x2y + xy2 + y3 + x3y
+ x3y + x2y2 + xy3 + y4 + ……….
(1) – (2) ⇒
Class 10 Maths Chapter 2 Exercise 2.8 Samacheer Kalvi