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Direction for questions 1 to 2 : Read passage below and solve the questions based on it.
Tn a horticultural show, a participant arranged a total of 1000 fruits of four types in a long straight line He first placed one apple, then two mangoes, three oranges, four custard apples, five apples, six mangoes, seven oranges, eight custard apples and so on (with apples followed by mangoes, oranges, custard apples in that order) uplo the 1000th fruit.
What was the 1000th fruit?
  • a)
    Apple
  • b)
    Mango
  • c)
    Orange
  • d)
    Custard apple
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Direction for questions 1 to 2 : Read passage below and solve the ques...
Fruits are ordered like 1. Apple 2. Mangoes 3 Oranges 4. Custard apple Fruits arc being pul up first one. then two, then three, then four and so oil.
1 + 2 + 3 + ... +44 = 990
So, the 45th fruit will be the 100th fruit. Since we are having a set of four different types of fruits, 45th will be Apple.
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Direction for questions 1 to 2 : Read passage below and solve the ques...
Explanation:

The participant arranged the fruits in a specific pattern. Let's analyze the pattern to determine the 1000th fruit.

Pattern Analysis:

The participant placed one apple, then two mangoes, three oranges, four custard apples, and continued this sequence.

1. First Iteration:
- 1st fruit: Apple
- 2nd fruit: Mango
- 3rd fruit: Mango
- 4th fruit: Orange
- 5th fruit: Orange
- 6th fruit: Orange
- 7th fruit: Custard apple
- 8th fruit: Custard apple
- 9th fruit: Custard apple
- 10th fruit: Custard apple

2. Second Iteration:
- 11th fruit: Apple
- 12th fruit: Apple
- 13th fruit: Mango
- 14th fruit: Mango
- 15th fruit: Mango
- 16th fruit: Orange
- 17th fruit: Orange
- 18th fruit: Orange
- 19th fruit: Orange
- 20th fruit: Custard apple
- ...

Pattern Conclusion:

The pattern continues, with each fruit type increasing by one in each iteration. The number of fruits in each iteration follows the sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...

Determining the 1000th fruit:

To determine the 1000th fruit, we need to find the iteration in which the 1000th fruit falls and the position of the fruit within that iteration.

1. Finding the iteration:
- The sum of the first n terms of a sequence is given by the formula: S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.
- In this case, the sum of the first n terms is 1000. We can start checking for n = 1, 2, 3, ... until we find the iteration where the sum exceeds 1000.
- For n = 1, the sum is 1. For n = 2, the sum is 3. For n = 3, the sum is 6. For n = 4, the sum is 10. For n = 5, the sum is 15. For n = 6, the sum is 21. For n = 7, the sum is 28. For n = 8, the sum is 36. For n = 9, the sum is 45. For n = 10, the sum is 55. For n = 11, the sum is 66. For n = 12, the sum is 78. For n = 13, the sum is 91. For n = 14, the sum is 105. For n = 15, the sum is 120. For n = 16, the sum is 136. For n = 17, the sum is 153. For n = 18
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Direction for questions 1 to 2 : Read passage below and solve the questions based on it.Tn a horticultural show, a participant arranged a total of 1000 fruits of four types in a long straight line He first placed one apple, then two mangoes, three oranges, four custard apples, five apples, six mangoes, seven oranges, eight custard apples and so on (with apples followed by mangoes, oranges, custard apples in that order) uplo the 1000th fruit.What was the 1000th fruit?a)Appleb)Mangoc)Oranged)Custard appleCorrect answer is option 'A'. Can you explain this answer?
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