NCERT Class X Chapter 5: Arithmetic Progression Example 16(ii)
NCERT Class X Chapter 5: Arithmetic Progression Example 16(ii) 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 production in the 10th year Given: Production in the 3rd year = 600 sets Production in the 7th year = 700 sets To Find: Production in the 10th year Formula: Let the production in the nth year be given by the arithmetic progression: a n = a 1 + (n-1)d, where a 1 is the production in the first year and d is the common difference. Solution: Let a 3 = 600 and a 7 = 700. Then we have: a 3 = a 1 + 2d = 600 ⇒ a 1 = 600 - 2d a 7 = a 1 + 6d = 700 Substituting a 1 = 600 - 2d: (600 - 2d) + 6d = 700 4d = 100 d = 25 Now, we find a 1 : a 1 = 600 - 2(25) = 600 - 50 = 550 Finally, we find a 10 : a 10 = a 1 + 9d = 550 + 9(25) = 550 + 225 = 775 Result: The production in the 10th yea...