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Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ is
- a)n2 (2n2 – 1)
- b)n3 (n – 1)
- c)n3 + 8n + 4
- d)2n4 + 3n2
Correct answer is option 'A'. Can you explain this answer?
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Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ is...
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Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ is...
The given series can be written as:
13, 33, 53, 73, ...
We can observe that each term is obtained by adding 20 to the previous term.
So, the nth term of the series can be represented as:
a_n = a_1 + (n-1)d
where a_1 = 13 (first term), d = 20 (common difference), and n is the number of terms.
To find the sum of the n terms, we can use the formula for the sum of an arithmetic series:
S_n = (n/2)(2a_1 + (n-1)d)
Substituting the given values, we have:
S_n = (n/2)(2(13) + (n-1)(20))
Simplifying further:
S_n = (n/2)(26 + 20n - 20)
S_n = (n/2)(20n + 6)
S_n = 10n^2 + 3n
Therefore, the sum of the n terms of the given series is given by the expression 10n^2 + 3n.
13, 33, 53, 73, ...
We can observe that each term is obtained by adding 20 to the previous term.
So, the nth term of the series can be represented as:
a_n = a_1 + (n-1)d
where a_1 = 13 (first term), d = 20 (common difference), and n is the number of terms.
To find the sum of the n terms, we can use the formula for the sum of an arithmetic series:
S_n = (n/2)(2a_1 + (n-1)d)
Substituting the given values, we have:
S_n = (n/2)(2(13) + (n-1)(20))
Simplifying further:
S_n = (n/2)(26 + 20n - 20)
S_n = (n/2)(20n + 6)
S_n = 10n^2 + 3n
Therefore, the sum of the n terms of the given series is given by the expression 10n^2 + 3n.
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Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ isa)n2 (2n2 – 1)b)n3 (n – 1)c)n3 + 8n + 4d)2n4 + 3n2Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ isa)n2 (2n2 – 1)b)n3 (n – 1)c)n3 + 8n + 4d)2n4 + 3n2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ isa)n2 (2n2 – 1)b)n3 (n – 1)c)n3 + 8n + 4d)2n4 + 3n2Correct answer is option 'A'. Can you explain this answer?.
Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ isa)n2 (2n2 – 1)b)n3 (n – 1)c)n3 + 8n + 4d)2n4 + 3n2Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ isa)n2 (2n2 – 1)b)n3 (n – 1)c)n3 + 8n + 4d)2n4 + 3n2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sum of n terms of the following series 13 + 33 + 53 + 73 + ........ isa)n2 (2n2 – 1)b)n3 (n – 1)c)n3 + 8n + 4d)2n4 + 3n2Correct answer is option 'A'. Can you explain this answer?.
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