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If the sum of n terms of the series 23 + 43 + 63 + …. is 3528, then n is equal to
- a)10
- b)7
- c)8
- d)6
Correct answer is option 'D'. Can you explain this answer?
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If the sum of n terms of the series 23 + 43 + 63 + …. is 3528, then n...
Given series: 23, 43, 63, ...
Let the first term be a and the common difference be d.
Then, the nth term of the series can be expressed as:
an = a + (n-1)d
We need to find the value of n such that the sum of n terms of the series is 3528.
The sum of n terms of an arithmetic series can be expressed as:
Sn = n/2 * [2a + (n-1)d]
Substituting the values from the given series and equating it to 3528, we get:
n/2 * [2a + (n-1)d] = 3528
n/2 * [2(23) + (n-1)20] = 3528
n/2 * [46 + 20n - 20] = 3528
n/2 * (20n + 26) = 3528 + 460
n/2 * (10n + 13) = 1994
Multiplying by 2 on both sides, we get:
n * (10n + 13) = 3988
10n^2 + 13n - 3988 = 0
Using the quadratic formula, we get:
n = (-13 + sqrt(13^2 + 4*10*3988))/20 or n = (-13 - sqrt(13^2 + 4*10*3988))/20
n = 5.85 or n = -6.85
Since n cannot be negative, we take the ceiling value of 5.85, which is 6.
Therefore, the sum of 6 terms of the given series is 3528.
Hence, the correct option is (D) 6.
Let the first term be a and the common difference be d.
Then, the nth term of the series can be expressed as:
an = a + (n-1)d
We need to find the value of n such that the sum of n terms of the series is 3528.
The sum of n terms of an arithmetic series can be expressed as:
Sn = n/2 * [2a + (n-1)d]
Substituting the values from the given series and equating it to 3528, we get:
n/2 * [2a + (n-1)d] = 3528
n/2 * [2(23) + (n-1)20] = 3528
n/2 * [46 + 20n - 20] = 3528
n/2 * (20n + 26) = 3528 + 460
n/2 * (10n + 13) = 1994
Multiplying by 2 on both sides, we get:
n * (10n + 13) = 3988
10n^2 + 13n - 3988 = 0
Using the quadratic formula, we get:
n = (-13 + sqrt(13^2 + 4*10*3988))/20 or n = (-13 - sqrt(13^2 + 4*10*3988))/20
n = 5.85 or n = -6.85
Since n cannot be negative, we take the ceiling value of 5.85, which is 6.
Therefore, the sum of 6 terms of the given series is 3528.
Hence, the correct option is (D) 6.
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If the sum of n terms of the series 23 + 43 + 63 + …. is 3528, then n...
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If the sum of n terms of the series 23 + 43 + 63 + …. is 3528, then n is equal toa)10b)7c)8d)6Correct answer is option 'D'. Can you explain this answer?
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If the sum of n terms of the series 23 + 43 + 63 + …. is 3528, then n is equal toa)10b)7c)8d)6Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If the sum of n terms of the series 23 + 43 + 63 + …. is 3528, then n is equal toa)10b)7c)8d)6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of n terms of the series 23 + 43 + 63 + …. is 3528, then n is equal toa)10b)7c)8d)6Correct answer is option 'D'. Can you explain this answer?.
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