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The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is?
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The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is?
The sum of the series 3 1/2, 7, 10 1/2, 14 to the 17 terms is
To find the sum of the given series, we need to identify the pattern and use the formula for the sum of an arithmetic series.
Pattern of the series:
- The series starts with 3 1/2 and increases by 3 1/2 after each term.
- The common difference between each term is 3 1/2.
Formula for the sum of an arithmetic series:
The sum (S) of an arithmetic series with n terms can be calculated using the formula:
S = (n/2) * (2a + (n-1)d)
where a is the first term, d is the common difference, and n is the number of terms.
Applying the formula:
In the given series,
- a = 3 1/2 (first term)
- d = 3 1/2 (common difference)
- n = 17 (number of terms)
Using the formula, we can calculate the sum of the series.
Calculations:
S = (17/2) * (2 * 3 1/2 + (17-1) * 3 1/2)
= (17/2) * (7 + 16 * 3 1/2)
= (17/2) * (7 + 56 + 1/2)
= (17/2) * (63 1/2)
= (17/2) * (127/2)
= 17 * 127 / 4
= 2159 / 4
= 539.75
Therefore, the sum of the series 3 1/2, 7, 10 1/2, 14 to the 17 terms is 539.75.
To find the sum of the given series, we need to identify the pattern and use the formula for the sum of an arithmetic series.
Pattern of the series:
- The series starts with 3 1/2 and increases by 3 1/2 after each term.
- The common difference between each term is 3 1/2.
Formula for the sum of an arithmetic series:
The sum (S) of an arithmetic series with n terms can be calculated using the formula:
S = (n/2) * (2a + (n-1)d)
where a is the first term, d is the common difference, and n is the number of terms.
Applying the formula:
In the given series,
- a = 3 1/2 (first term)
- d = 3 1/2 (common difference)
- n = 17 (number of terms)
Using the formula, we can calculate the sum of the series.
Calculations:
S = (17/2) * (2 * 3 1/2 + (17-1) * 3 1/2)
= (17/2) * (7 + 16 * 3 1/2)
= (17/2) * (7 + 56 + 1/2)
= (17/2) * (63 1/2)
= (17/2) * (127/2)
= 17 * 127 / 4
= 2159 / 4
= 539.75
Therefore, the sum of the series 3 1/2, 7, 10 1/2, 14 to the 17 terms is 539.75.
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The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is?
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The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is?.
The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the series 3 1/2 7 10 1/2 14 .to the 17 terms is?.
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