Arithmetic Progression
Question 2 Deleted for CBSE Board 2025 Exams
Question 3 Important Deleted for CBSE Board 2025 Exams You are here
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
Arithmetic Progression
Last updated at April 16, 2024 by Teachoo
Ex9.2 , 3 In an A.P, the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is 112. It is given that First term = a = 2 Also Sum of first five terms = 1/4 (Sum of next 5 terms) Sum of first five terms = 1/4 (Sum of 6th to 10th terms) Sum of first five terms = 1/4 ( 8( ("Sum of first 10 terms " @" Sum of first five terms" ))) S5 = 1/4(S10 S5) 4S5 = S10 S5 4S5 + S5 = S10 5S5 = S10 Finding sum of first five terms We know that Sum of n terms of A.P. = /2(2a + (n 1)d) Sn = /2(2a + (n 1)d) Putting a = 2, n = 5 S5 = 5/2 (2(2) + (5 1)d) = 5/2 (4 + 4d) = 5/2 (4) + 5/2 (4)d = 10 + 10d Finding sum of first ten terms Sn = /2(2a + (n 1)d) Putting a = 2, n = 10 S10 = 10/2 (2(2) + (10 1)d) = 10/2 (4 + 9d) = 5(4 + 9d) = 20 + 45d From equation (1) 5S5 = S10 Putting values 5(10 + 10d) = 20 + 45d 50 + 50d = 20 + 45d 50d 45d = 20 50 5d = 30 d = ( 30)/5 = 6 To find 20th term, we use the formula an = a + (n 1)d where an = nth term , n = number of terms, a = first term , d = common difference Here, a = 2 , d = 6 , n = 20 Putting values a20 = 2 + (20 1) ( 6) = 2 + (19)(-6) = 2 114 = 112 Thus, 20th term of sequence is 112 Hence proved.