Arithmetic Progression

Chapter 8 Class 11 Sequences and Series
Serial order wise

### Transcript

Ex 9.2 , 18 The difference between any two consecutive interior angles of a polygon is 5 . If the smallest angle is 120 , find the number of the sides of the polygon. Difference between consecutive angles = 5 Smallest angle = 120 Second smallest angle = 120 + 5 = 125 Third smallest angle = 125 + 5 = 130 Thus, the angles are 120, 125,130, . The angles form an A.P. as difference of consecutive terms is constant. Here, first term = a = 120 Common difference = 125 120 For A.P., Sn = n/2 ( 2a + (n 1)d ) Where, Sn = sum of n terms of A.P. n = number of terms a = first term and d = common difference Here, Sn = Sum of all angles of polygon , a = 120, d = 5 Sn = n/2 (2(120) + (n 1)5) Also, Sum of all angles of a polygon with n sides= 180 (n 2). Sn = 180 (n 2) Comparing (1) & (2) n/2 (2(120) + (n 1)5) = 180 (n 2) n[240 + (n 1)5] = 180 2(n 2) n[240 + (n 1)5 ] = 360(n 2) 240n + 5n2 5n = 360n 720 5n2 + 235n 360n + 720 = 0 5n2 125n + 720 = 0 5(n2 25n + 144) = 0 (n2 25n + 144) = 0/5 n2 25n + 144 = 0 n2 16n 9n + 144 = 0 n(n 16) 9 (n 16) = 0 (n 9) (n 16) = 0 n = 9 or 16 Number of sides = 9 or 16

Made by

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.