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Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.
- a)5 + 10 + 15 + 20 + 25 + …… + xn
- b)5 + 10 + 15 + 20 + 25 + …… + 5n
- c)5 + 10 + 15 + 20 + 25 + …… + 5n + 1
- d)5 + 10 + 15 + 20 + 25 + …… + 6n
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ...
Given sequence: 5, 10, 15, 20, 25, ……, xn.
Therefore, the arithmetic series for the given sequence is 5 + 10 + 15 + 20 + 25 + …… + xn.
Community Answer
Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ...
Understanding the Arithmetic Series
The given sequence is an arithmetic series: 5, 10, 15, 20, 25, …, xn. An arithmetic series is characterized by a constant difference between consecutive terms, known as the common difference.
Identifying the Sequence
- The first term (a) is 5.
- The common difference (d) is 5 (10 - 5 = 5).
General Term of the Series
- The n-th term of an arithmetic series can be expressed as:
- xn = a + (n - 1)d
- For our series: xn = 5 + (n - 1) * 5 = 5n.
Sum of the Series
To find the sum of the series from the first term up to the n-th term, we use the formula for the sum (S) of the first n terms of an arithmetic series:
- S_n = n/2 * (first term + last term)
- In our case, the last term is 5n. Thus, the sum becomes:
- S_n = n/2 * (5 + 5n)
Evaluating the Options
Now, let’s evaluate the options given:
a) 5 + 10 + 15 + 20 + 25 + … + xn
- This correctly represents the sum of the series with the first term being 5 and the last term being xn.
b) 5 + 10 + 15 + 20 + 25 + … + 5n
- This is incorrect because it does not include the last term xn explicitly.
c) 5 + 10 + 15 + 20 + 25 + … + 5n + 1
- This is incorrect as it adds an unnecessary term.
d) 5 + 10 + 15 + 20 + 25 + … + 6n
- This is also incorrect as 6n does not correspond to the series.
Conclusion
The correct answer is option 'A', as it accurately reflects the arithmetic series from the first term to the n-th term (xn).
The given sequence is an arithmetic series: 5, 10, 15, 20, 25, …, xn. An arithmetic series is characterized by a constant difference between consecutive terms, known as the common difference.
Identifying the Sequence
- The first term (a) is 5.
- The common difference (d) is 5 (10 - 5 = 5).
General Term of the Series
- The n-th term of an arithmetic series can be expressed as:
- xn = a + (n - 1)d
- For our series: xn = 5 + (n - 1) * 5 = 5n.
Sum of the Series
To find the sum of the series from the first term up to the n-th term, we use the formula for the sum (S) of the first n terms of an arithmetic series:
- S_n = n/2 * (first term + last term)
- In our case, the last term is 5n. Thus, the sum becomes:
- S_n = n/2 * (5 + 5n)
Evaluating the Options
Now, let’s evaluate the options given:
a) 5 + 10 + 15 + 20 + 25 + … + xn
- This correctly represents the sum of the series with the first term being 5 and the last term being xn.
b) 5 + 10 + 15 + 20 + 25 + … + 5n
- This is incorrect because it does not include the last term xn explicitly.
c) 5 + 10 + 15 + 20 + 25 + … + 5n + 1
- This is incorrect as it adds an unnecessary term.
d) 5 + 10 + 15 + 20 + 25 + … + 6n
- This is also incorrect as 6n does not correspond to the series.
Conclusion
The correct answer is option 'A', as it accurately reflects the arithmetic series from the first term to the n-th term (xn).
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Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.a)5 + 10 + 15 + 20 + 25 + …… + xnb)5 + 10 + 15 + 20 + 25 + …… + 5nc)5 + 10 + 15 + 20 + 25 + …… + 5n + 1d)5 + 10 + 15 + 20 + 25 + …… + 6nCorrect answer is option 'A'. Can you explain this answer? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.a)5 + 10 + 15 + 20 + 25 + …… + xnb)5 + 10 + 15 + 20 + 25 + …… + 5nc)5 + 10 + 15 + 20 + 25 + …… + 5n + 1d)5 + 10 + 15 + 20 + 25 + …… + 6nCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.a)5 + 10 + 15 + 20 + 25 + …… + xnb)5 + 10 + 15 + 20 + 25 + …… + 5nc)5 + 10 + 15 + 20 + 25 + …… + 5n + 1d)5 + 10 + 15 + 20 + 25 + …… + 6nCorrect answer is option 'A'. Can you explain this answer?.
Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.a)5 + 10 + 15 + 20 + 25 + …… + xnb)5 + 10 + 15 + 20 + 25 + …… + 5nc)5 + 10 + 15 + 20 + 25 + …… + 5n + 1d)5 + 10 + 15 + 20 + 25 + …… + 6nCorrect answer is option 'A'. Can you explain this answer? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.a)5 + 10 + 15 + 20 + 25 + …… + xnb)5 + 10 + 15 + 20 + 25 + …… + 5nc)5 + 10 + 15 + 20 + 25 + …… + 5n + 1d)5 + 10 + 15 + 20 + 25 + …… + 6nCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.a)5 + 10 + 15 + 20 + 25 + …… + xnb)5 + 10 + 15 + 20 + 25 + …… + 5nc)5 + 10 + 15 + 20 + 25 + …… + 5n + 1d)5 + 10 + 15 + 20 + 25 + …… + 6nCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Write the arithmetic series for the given sequence 5, 10, 15, 20, 25, ….., xn.a)5 + 10 + 15 + 20 + 25 + …… + xnb)5 + 10 + 15 + 20 + 25 + …… + 5nc)5 + 10 + 15 + 20 + 25 + …… + 5n + 1d)5 + 10 + 15 + 20 + 25 + …… + 6nCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 8.
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