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Which of the following is the correct value of given number expression: (22 + 42 + 62 + ... + 202) = ?
- a)77 × 10
- b)231 × 5
- c)2 × 77 × 10
- d)385 × 385
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which of the following is the correct value of given number expression...
(22 + 42 + 62 + ... + 202)
= (1 × 2)2 + (2 × 2)2 + (2 × 3)2 + ... + (2 × 10)2
= (22 × 12) + (22 × 22) + (22 × 32) + ...
+ (22 × 102)
= 22 × [12 + 22 + 32 + ... + 102]
[Formula: (12 + 22 + 32 + ... + n2)
= (4 × 5 × 77)
= 2 × 77 × 10
= (1 × 2)2 + (2 × 2)2 + (2 × 3)2 + ... + (2 × 10)2
= (22 × 12) + (22 × 22) + (22 × 32) + ...
+ (22 × 102)
= 22 × [12 + 22 + 32 + ... + 102]
[Formula: (12 + 22 + 32 + ... + n2)
= (4 × 5 × 77)
= 2 × 77 × 10
Most Upvoted Answer
Which of the following is the correct value of given number expression...
Calculation of the given number expression:
First, let's identify the pattern in the given number expression. The numbers in the expression are 22, 42, 62, ..., 202. These numbers can be written as 2^2, 4^2, 6^2, ..., 20^2.
Finding the sum of squares:
To find the sum of squares from 2^2 to 20^2, we can use the formula for the sum of squares of the first n natural numbers: n(n+1)(2n+1)/6.
Let n = 10 (as there are 10 terms from 2^2 to 20^2).
Sum = 10(10+1)(2*10+1)/6
Sum = 10*11*21/6
Sum = 10*77
Sum = 770
Expression in terms of 77:
Now, we have found that the sum of squares from 2^2 to 20^2 is 770.
Given expression can be written as (22 + 42 + 62 + ... + 202) = 77*10 = 770.
Therefore, the correct value of the given number expression is 2 * 77 * 10 = 1540. Hence, option 'C' is the correct answer.
First, let's identify the pattern in the given number expression. The numbers in the expression are 22, 42, 62, ..., 202. These numbers can be written as 2^2, 4^2, 6^2, ..., 20^2.
Finding the sum of squares:
To find the sum of squares from 2^2 to 20^2, we can use the formula for the sum of squares of the first n natural numbers: n(n+1)(2n+1)/6.
Let n = 10 (as there are 10 terms from 2^2 to 20^2).
Sum = 10(10+1)(2*10+1)/6
Sum = 10*11*21/6
Sum = 10*77
Sum = 770
Expression in terms of 77:
Now, we have found that the sum of squares from 2^2 to 20^2 is 770.
Given expression can be written as (22 + 42 + 62 + ... + 202) = 77*10 = 770.
Therefore, the correct value of the given number expression is 2 * 77 * 10 = 1540. Hence, option 'C' is the correct answer.
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Which of the following is the correct value of given number expression: (22 + 42 + 62 + ... + 202) = ?a)77 × 10b)231 × 5c)2 × 77 × 10d)385 × 385Correct answer is option 'C'. Can you explain this answer?
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Which of the following is the correct value of given number expression: (22 + 42 + 62 + ... + 202) = ?a)77 × 10b)231 × 5c)2 × 77 × 10d)385 × 385Correct answer is option 'C'. Can you explain this answer? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Which of the following is the correct value of given number expression: (22 + 42 + 62 + ... + 202) = ?a)77 × 10b)231 × 5c)2 × 77 × 10d)385 × 385Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is the correct value of given number expression: (22 + 42 + 62 + ... + 202) = ?a)77 × 10b)231 × 5c)2 × 77 × 10d)385 × 385Correct answer is option 'C'. Can you explain this answer?.
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