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Arithmetic Progressions
CH05 Question Bank
CBSE_CH05_QUESTION_BANK
Grade 10

Question:

A manufacturer of TV sets produces 600 units in the third year and 700 units in the seventh year. Assuming that the production increases uniformly by a fixed number of units every year (forming an AP), find the production in the first year and the annual increase.

Step-by-Step Solution

Key Concept: Model yearly production as an AP; use the given two terms to form and solve simultaneous equations.
$a_3=600\Rightarrow a+2d=600$ — (1). $a_7=700\Rightarrow a+6d=700$ — (2). [1.0 Mark]

Subtracting (1) from (2): $4d=100\Rightarrow d=25$. [1.0 Mark]

From (1): $a=600-50=550$. So production in the first year is $550$ units, increasing by $25$ units each year. [1.0 Mark]

Correct Answer:
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