NCERT solution Class 10 arithmetic progressions

NCERT Solutions

Class 10 Maths

Arithmetic Progressions

NCERT Questions

Ex. 5.1 Q.1
Ex. 5.1 Q.2
Ex. 5.1 Q.3
Ex. 5.1 Q.4
Ex. 5.2 Q.1
Ex. 5.2 Q.2
Ex. 5.2 Q.3
Ex. 5.2 Q.4
Ex. 5.2 Q.5
Ex. 5.2 Q.6
Ex. 5.2 Q.7
Ex. 5.2 Q.8
Ex. 5.2 Q.9
Ex. 5.2 Q.10
Ex. 5.2 Q.11
Ex. 5.2 Q.12
Ex. 5.2 Q.13
Ex. 5.2 Q.14
Ex. 5.2 Q.15
Ex. 5.2 Q.16
Ex. 5.2 Q.17
Ex. 5.2 Q.18
Ex. 5.2 Q.19
Ex. 5.2 Q.20
Ex. 5.3 Q.1
Ex. 5.3 Q.2
Ex. 5.3 Q.3
Ex. 5.3 Q.4
Ex. 5.3 Q.5
Ex. 5.3 Q.6
Ex. 5.3 Q.7
Ex. 5.3 Q.8
Ex. 5.2 Q.9
Ex. 5.3 Q.10
Ex. 5.3 Q.11
Ex. 5.2 Q.12
Ex. 5.3 Q.13
Ex. 5.3 Q.14
Ex. 5.3 Q.15
Ex. 5.3 Q.16
Ex. 5.3 Q.17
Ex. 5.3 Q.18
Ex. 5.3 Q.19
Ex. 5.3 Q.20
Ex. 5.4 Q.1
Ex. 5.4 Q.2
Ex. 5.4 Q.3
Ex. 5.4 Q.4
Ex. 5.4 Q.5

Ex. 5.4 Q.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.

Let first term of AP = a

Common difference of AP = d

Given, 3^rd term + 7^th term = 6

=> a + 2d + a + 6d = 6

=> 2a + 8d = 6

=> a + 4d = 3.......................1

Again given 3^rd term * 7^th term = 8

=> (a + 2d) * (a + 6d) = 8

=> a² + 8ad + 12d² = 8.............2 From equation 1, we get

a + 4d =3

=> a = 3 - 4d ...................3

Put value of a in equation 2, we get

(3 - 4d)² + 8*(3 - 4d)*d + 12d² = 8

=> 9 + 16d² - 24d + 24d - 32d² + 12d² = 8

=> 9 - 4d² = 8

=> 4d² = 9 - 8

=> 4d² = 1

=> d² = 1/4

=> d = ±√(1/4)

=> d = 1/2, -1/2

Now put this value in equation 3

=> a = 3 - 4*(1/2) and a = 3 - 4*(-1/2)

=> a = 3 - 2 and a = 3 + 2

=> a = 1, 5

Case 1: when a = 1, d = 1/2

Sum of first 16 terms = (n/2) *{2a + (n-1)*d}

= (16/2)*{2*1 + (16-1)*1/2}

= 8*(2 + 15/2)

= 8*(2 + 7.5)

= 8*9.5

= 76

Case 2: when a = 5, d = -1/2

Sum of first 16 terms = (n/2) *{2a + (n-1)*d}

= (16/2)*{2*5 + (16-1)*(-1/2)}

= 8*(10 - 15/2)

= 8*(10 - 7.5)

= 8 * 2.5

= 20

Video solution:

Arithmetic Progressions Class 10 Maths NCERT Chapter 5 NCERT Solutions

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NCERT solutions of Arithmetic Progressions Class 10 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 10 Maths Arithmetic Progressions NCERT solutions.