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Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?
the answer is 48. Can anyone explain how?
the answer is 48. Can anyone explain how?
Verified Answer
Let a sequence have 1000 zeroes. Instep 1, to every position in the se...
Let the sequence be a₁,a₂,a₃,a₄,a₅,.a₁₀₀₀.
Step 1: Every position in the sequence is increased by 2.
Step 2: Every even position in the sequence is increased by 2.
Step 3: Every 3rd term in the sequence is increased by 2.
a₁ is added by 2 only in step 1
a₂ is added by 2 in steps 1 and 2
a₃ is added by 2 in steps 1 and 3
Clearly it is evident that any term aₓ is added by 2 in step n ,
if and only if n is the factor of x.
Now, if we factorize 600 we get , 600 =2^3X3X5^2.
Thus total number of factors of 600 are (1+3)X(1+1)X(1+2) = 24.
So, during each of these 24 steps a₆₀₀ will be added by 2.
Thus a₆₀₀ would be added by 2 24 times , hence a₆₀₀ would be
increased by 24X2 = 48.
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Most Upvoted Answer
Let a sequence have 1000 zeroes. Instep 1, to every position in the se...
Explanation:
To find the value in the 600th position after 1000 steps, we need to understand the pattern of adding 2 to different positions in each step.
Step 1:
In the first step, we add 2 to every position in the sequence. Since the sequence initially consists of 1000 zeroes, after this step, all positions will have a value of 2.
Step 2:
In the second step, we add 2 to every even position in the sequence. Since all positions have a value of 2 after the first step, only the even positions will have their values increased to 4. The odd positions will remain at 2.
Step 3:
In the third step, we add 2 to every position which is a multiple of 3. Since the positions are numbered from 1 to 1000, the positions that are multiples of 3 are 3, 6, 9, 12, and so on. Therefore, the values in these positions will be increased to 6.
Step 4:
In the fourth step, we add 2 to every position which is a multiple of 4. The positions that are multiples of 4 are 4, 8, 12, 16, and so on. Therefore, the values in these positions will be increased to 8.
This pattern continues for each subsequent step, with the values in positions that are multiples of the step number being increased by 2.
600th position:
To find the value in the 600th position after 1000 steps, we need to determine which steps affect this position.
- Step 1: The value in position 600 is increased to 2.
- Step 2: The value in position 600 remains at 2 since it is an odd position.
- Step 3: The value in position 600 remains at 2 since it is not a multiple of 3.
- Step 4: The value in position 600 remains at 2 since it is not a multiple of 4.
Following this pattern, we can see that the value in position 600 will remain at 2 throughout the 1000 steps.
Therefore, the final value in the 600th position after 1000 steps will be 2.
To find the value in the 600th position after 1000 steps, we need to understand the pattern of adding 2 to different positions in each step.
Step 1:
In the first step, we add 2 to every position in the sequence. Since the sequence initially consists of 1000 zeroes, after this step, all positions will have a value of 2.
Step 2:
In the second step, we add 2 to every even position in the sequence. Since all positions have a value of 2 after the first step, only the even positions will have their values increased to 4. The odd positions will remain at 2.
Step 3:
In the third step, we add 2 to every position which is a multiple of 3. Since the positions are numbered from 1 to 1000, the positions that are multiples of 3 are 3, 6, 9, 12, and so on. Therefore, the values in these positions will be increased to 6.
Step 4:
In the fourth step, we add 2 to every position which is a multiple of 4. The positions that are multiples of 4 are 4, 8, 12, 16, and so on. Therefore, the values in these positions will be increased to 8.
This pattern continues for each subsequent step, with the values in positions that are multiples of the step number being increased by 2.
600th position:
To find the value in the 600th position after 1000 steps, we need to determine which steps affect this position.
- Step 1: The value in position 600 is increased to 2.
- Step 2: The value in position 600 remains at 2 since it is an odd position.
- Step 3: The value in position 600 remains at 2 since it is not a multiple of 3.
- Step 4: The value in position 600 remains at 2 since it is not a multiple of 4.
Following this pattern, we can see that the value in position 600 will remain at 2 throughout the 1000 steps.
Therefore, the final value in the 600th position after 1000 steps will be 2.
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Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how?
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Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how?.
Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how?.
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Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how?, a detailed solution for Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how? has been provided alongside types of Let a sequence have 1000 zeroes. Instep 1, to every position in the sequence we add 2. Instep 2, to every even position in the sequence we add 2. Instep 3, to every position which is a multiple of 3 we add 2. This is continues up to 1000th step. After 1000th step, what will be the value in the 600th position?the answer is 48. Can anyone explain how? theory, EduRev gives you an
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