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Ex 5.3

Ex 5.3, 1 (i)

Ex 5.3, 1 (ii)

Ex 5.3, 1 (iii) Important

Ex 5.3, 1 (iv)

Ex 5.3, 2 (i)

Ex 5.3, 2 (ii)

Ex 5.3, 2 (iii) Important

Ex 5.3, 3 (i)

Ex 5.3, 3 (ii)

Ex 5.3, 3 (iii)

Ex 5.3, 3 (iv) Important

Ex 5.3, 3 (v)

Ex 5.3, 3 (vi) Important

Ex 5.3, 3 (vii)

Ex 5.3, 3 (viii) Important

Ex 5.3, 3 (ix)

Ex 5.3, 3 (x)

Ex 5.3, 4 You are here

Ex 5.3, 5

Ex 5.3, 6 Important

Ex 5.3, 7

Ex 5.3, 8

Ex 5.3, 9

Ex 5.3, 10 (i)

Ex 5.3, 10 (ii) Important

Ex 5.3, 11 Important

Ex 5.3, 12

Ex 5.3, 13

Ex 5.3, 14 Important

Ex 5.3, 15

Ex 5.3, 16 Important

Ex 5.3, 17

Ex 5.3, 18 Important

Ex 5.3, 19 Important

Ex 5.3, 20 Important

Chapter 5 Class 10 Arithmetic Progressions

Serial order wise

Last updated at May 29, 2023 by Teachoo

Ex 5.3, 4 How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636? Given AP is 9, 17, 25, ….. Here, a = 9 d = 17 – 9 = 8 & Sum = Sn = 636 We need to find n We know that Sum = 𝑛/2 (2a + (n – 1) d) Putting a = 9, d = 8, Sn = 636 636 = 𝑛/(2 ) (2 × 9 + (n – 1) × 8) 636 × 2 = n (18 + 8n – 8) 1272 = n (10 + 8n) 1272 = 10n + 8n2 0 = 10n + 8n2 – 1272 10n + 8n2 – 1272 = 0 2(5n + 4n2 – 636)= 0 5n + 4n2 – 636 = 0 4n2 + 5n – 636 = 0 We solve by quadratic formula Comparing equation with ax2 + bx + c = 0 Here, a = 4, b = 5, c = – 636 We know that, D = b2 – 4ac D = (5)2 – 4 × 4 × (–636) D = 25 + 10176 D = 10201 Hence, roots to equation are given by n = (− 𝒃 ± √𝑫)/𝟐𝒂 Putting values n = (− 5 ± √𝟏𝟎𝟐𝟎𝟏)/(2 × 4) n = (− 𝟓 ± 𝟏𝟎𝟏)/𝟖 Finding root of 10201 10201 = 101 × 101 10201 = 1012 So, √("10201" ) = 101 Solving So, n = 12 & n = (−53)/4 Since n cannot be negative, ∴ n = 12 n = (−𝟓 + 𝟏𝟎𝟏)/𝟖 n = 96/8 n = 12 n = (−𝟓 − 𝟏𝟎𝟏)/𝟖 n = (−106)/8 n = (−𝟓𝟑)/𝟒