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Arithmetic Progressions
CBSE 2026 Board Exam Set 1 (Code 30/1/1)
CBSE_BOARD_PYQ_2026_30_1_1
Grade 10

Question:

[Section E]

Case Study 1: Production of TV Sets

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, answer the following questions:

1. Find the production in the $1^{\text{st}}$ year. (1 Mark)
2. Find the production in the $10^{\text{th}}$ year. (1 Mark)
3. Find the total production in first $7$ years. (2 Marks)

OR (for part 3)

3. In which year will the production reach $1000$ sets? (2 Marks)

Step-by-Step Solution

Key Concept: AP equations: $a + 2d = 600, a + 6d = 700 \Rightarrow d = 25, a = 550$.
1. $a = 550$ sets. [1.0 Mark]

2. $a_{10} = 550 + 9(25) = 775$ sets. [1.0 Mark]

[Part 3 Main] $S_7 = (7/2)[2(550) + 6(25)] = 4375$ sets. [2.0 Marks]


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[Part 3 OR Choice]
$550 + (n-1)25 = 1000 \Rightarrow n = 19^{\text{th}}$ year. [2.0 Marks]

Correct Answer: 1. 550 sets, 2. 775 sets, 3. 4375 sets (OR 19th year)
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