Arithmetic Progression
Question 2 Deleted for CBSE Board 2025 Exams
Question 3 Important Deleted for CBSE Board 2025 Exams
Question 4 Deleted for CBSE Board 2025 Exams
Question 5 Important Deleted for CBSE Board 2025 Exams
Question 6 Deleted for CBSE Board 2025 Exams
Question 7 Important Deleted for CBSE Board 2025 Exams
Question 8 Deleted for CBSE Board 2025 Exams
Question 9 Important Deleted for CBSE Board 2025 Exams
Question 10 Deleted for CBSE Board 2025 Exams
Question 11 Important Deleted for CBSE Board 2025 Exams
Question 12 Deleted for CBSE Board 2025 Exams
Question 13 Deleted for CBSE Board 2025 Exams
Question 14 Important Deleted for CBSE Board 2025 Exams
Question 15 Important Deleted for CBSE Board 2025 Exams
Question 16 Important Deleted for CBSE Board 2025 Exams
Question 17 Deleted for CBSE Board 2025 Exams
Question 18 Important Deleted for CBSE Board 2025 Exams You are here
Arithmetic Progression
Last updated at April 16, 2024 by Teachoo
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