NCERT Class X Chapter 5: Arithmetic Progression Example 16(iii)
NCERT Class X Chapter 5: Arithmetic Progression Example 16(iii) Question: A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find : the total production in first 7 years Given: Production in the 3rd year = 600 sets Production in the 7th year = 700 sets To Find: Total production in the first 7 years Formula: Arithmetic progression: a n = a 1 + (n-1)d , S n = n 2 (a 1 + a n ) Solution: Let a n be the production in the nth year. We are given that a 3 = 600 and a 7 = 700. Since the production increases uniformly, this forms an arithmetic progression. Using the formula a n = a 1 + (n-1)d, we have: a 3 = a 1 + 2d = 600 ⇒ a 1 + 2d = 600 (1) a 7 = a 1 + 6d = 700 ⇒ a 1 + 6d = 700 (2) Subtracting (1) from (2): 4d = 100 ⇒ d = 25 Substituting d = 25 in (1): a 1 + 2(25) = 6...