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If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?
(2019)
- a)4851
- b)4855
- c)4856
- d)4877
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what ...
Given:
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 5280
To find:
The value of 1 * 2 * 3 * ... * n
Solution:
Let's simplify the given expression step by step to find a pattern.
Step 1:
Let's rewrite the given expression as a product of consecutive odd numbers:
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 1 * 3 * 5 * ... * 47
Step 2:
We can rewrite the product of consecutive odd numbers as:
[(2n+1) * (2n+3) * (2n+5) * ... * (2n+47)] / [(1 * 3 * 5 * ... * 47)] = 1
Step 3:
Now, let's simplify the expression further by canceling out common factors:
[(2n+1) * (2n+3) * (2n+5) * ... * (2n+47)] / [(1 * 3 * 5 * ... * 47)] = 1
[(2n+1) / 1] * [(2n+3) / 3] * [(2n+5) / 5] * ... * [(2n+47) / 47] = 1
Step 4:
Simplifying each term:
[(2n+1) / 1] * [(2n+3) / 3] * [(2n+5) / 5] * ... * [(2n+47) / 47] = 1
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 1 * 3 * 5 * ... * 47
Step 5:
Since both sides of the equation are equal to the same value, we can equate them:
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 5280
1 * 3 * 5 * ... * 47 = 5280
Step 6:
Now, let's find the value of 1 * 2 * 3 * ... * n using the formula:
1 * 2 * 3 * ... * n = [(n+1)!] / 1
Step 7:
We know that 1 * 3 * 5 * ... * 47 = 5280
Therefore, [(n+1)!] / 1 = 5280
Step 8:
Simplifying the equation:
(n+1)! = 5280
Step 9:
From the given options, the only option that satisfies the equation (n+1)! = 5280 is n = 7.
Step 10:
Substituting n = 7 in the expression 1 * 2
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 5280
To find:
The value of 1 * 2 * 3 * ... * n
Solution:
Let's simplify the given expression step by step to find a pattern.
Step 1:
Let's rewrite the given expression as a product of consecutive odd numbers:
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 1 * 3 * 5 * ... * 47
Step 2:
We can rewrite the product of consecutive odd numbers as:
[(2n+1) * (2n+3) * (2n+5) * ... * (2n+47)] / [(1 * 3 * 5 * ... * 47)] = 1
Step 3:
Now, let's simplify the expression further by canceling out common factors:
[(2n+1) * (2n+3) * (2n+5) * ... * (2n+47)] / [(1 * 3 * 5 * ... * 47)] = 1
[(2n+1) / 1] * [(2n+3) / 3] * [(2n+5) / 5] * ... * [(2n+47) / 47] = 1
Step 4:
Simplifying each term:
[(2n+1) / 1] * [(2n+3) / 3] * [(2n+5) / 5] * ... * [(2n+47) / 47] = 1
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 1 * 3 * 5 * ... * 47
Step 5:
Since both sides of the equation are equal to the same value, we can equate them:
(2n+1) * (2n+3) * (2n+5) * ... * (2n+47) = 5280
1 * 3 * 5 * ... * 47 = 5280
Step 6:
Now, let's find the value of 1 * 2 * 3 * ... * n using the formula:
1 * 2 * 3 * ... * n = [(n+1)!] / 1
Step 7:
We know that 1 * 3 * 5 * ... * 47 = 5280
Therefore, [(n+1)!] / 1 = 5280
Step 8:
Simplifying the equation:
(n+1)! = 5280
Step 9:
From the given options, the only option that satisfies the equation (n+1)! = 5280 is n = 7.
Step 10:
Substituting n = 7 in the expression 1 * 2
Community Answer
If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what ...
The sequence (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280 is in A.P. with first term (a) = 2n + 1
common difference (d) = 2 and last term (l) = 2n + 47,
Let ‘m’ be the number of terms in this sequence, then
l = a + (m – 1)d
2n + 47 = (2n + 1) + (m – 1) (2) ⇒ m = 24
Now, (2n + 1) + (2n + 3) + (2n + 5) +....+ (2n + 47) = 5280
⇒ 24(2n + 1 + 23) = 48(n + 12) = 5280
⇒ 48(n + 12) = 5280
∴ n = 98 Now, 1 + 2 + 3 + ... +
common difference (d) = 2 and last term (l) = 2n + 47,
Let ‘m’ be the number of terms in this sequence, then
l = a + (m – 1)d
2n + 47 = (2n + 1) + (m – 1) (2) ⇒ m = 24
Now, (2n + 1) + (2n + 3) + (2n + 5) +....+ (2n + 47) = 5280
⇒ 24(2n + 1 + 23) = 48(n + 12) = 5280
⇒ 48(n + 12) = 5280
∴ n = 98 Now, 1 + 2 + 3 + ... +
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If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?(2019)a)4851b)4855c)4856d)4877Correct answer is option 'A'. Can you explain this answer?
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If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?(2019)a)4851b)4855c)4856d)4877Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?(2019)a)4851b)4855c)4856d)4877Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?(2019)a)4851b)4855c)4856d)4877Correct answer is option 'A'. Can you explain this answer?.
If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?(2019)a)4851b)4855c)4856d)4877Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?(2019)a)4851b)4855c)4856d)4877Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (2n + 1) + (2n + 3) + (2n + 5) + ... + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + ... + n?(2019)a)4851b)4855c)4856d)4877Correct answer is option 'A'. Can you explain this answer?.
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