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The sum of the series 5 + 9 + 13 + … + 49 is:
- a)351
- b)535
- c)324
- d)435
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)4...
Concept:
Arithmetic Progression (AP):
Arithmetic Progression (AP):
- The sequence of numbers where the difference of any two consecutive terms is same is called an Arithmetic Progression.
- If a be the first term, d be the common difference and n be the number of terms of an AP, then the sequence can be written as follows:
a, a + d, a + 2d, ..., a + (n - 1)d. - The sum of n terms of the above series is given by:
Calculation:
The given series is 5 + 9 + 13 + … + 49 which is an arithmetic progression with first term a = 5 and common difference d = 4.
Let's say that the last term 49 is the nth term.
∴ a + (n - 1)d = 49
⇒ 5 + 4(n - 1) = 49
⇒ 4(n - 1) = 44
⇒ n = 12.
And, the sum of this AP is:
The given series is 5 + 9 + 13 + … + 49 which is an arithmetic progression with first term a = 5 and common difference d = 4.
Let's say that the last term 49 is the nth term.
∴ a + (n - 1)d = 49
⇒ 5 + 4(n - 1) = 49
⇒ 4(n - 1) = 44
⇒ n = 12.
And, the sum of this AP is:
Most Upvoted Answer
The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)4...
Understanding the Series
The series given is 5 + 9 + 13 + ... + 49. This is an arithmetic series where the first term (a) is 5 and the common difference (d) is 4.
Identifying the Terms
To find the sum, we first need to determine the number of terms (n) in the series.
- The last term (l) of the series is 49.
- The nth term of an arithmetic series can be expressed as:
nth term = a + (n - 1) * d.
Setting up the equation for the last term:
- 49 = 5 + (n - 1) * 4.
- Solving for n:
49 - 5 = (n - 1) * 4,
44 = (n - 1) * 4,
n - 1 = 11,
n = 12.
Calculating the Sum of the Series
The formula for the sum (S) of the first n terms in an arithmetic series is:
S = n/2 * (a + l).
Substituting the values we found:
- n = 12,
- a = 5,
- l = 49.
Calculating the sum:
S = 12/2 * (5 + 49)
S = 6 * 54
S = 324.
Conclusion
Thus, the sum of the series 5 + 9 + 13 + ... + 49 is 324. Therefore, the correct answer is option 'C'.
The series given is 5 + 9 + 13 + ... + 49. This is an arithmetic series where the first term (a) is 5 and the common difference (d) is 4.
Identifying the Terms
To find the sum, we first need to determine the number of terms (n) in the series.
- The last term (l) of the series is 49.
- The nth term of an arithmetic series can be expressed as:
nth term = a + (n - 1) * d.
Setting up the equation for the last term:
- 49 = 5 + (n - 1) * 4.
- Solving for n:
49 - 5 = (n - 1) * 4,
44 = (n - 1) * 4,
n - 1 = 11,
n = 12.
Calculating the Sum of the Series
The formula for the sum (S) of the first n terms in an arithmetic series is:
S = n/2 * (a + l).
Substituting the values we found:
- n = 12,
- a = 5,
- l = 49.
Calculating the sum:
S = 12/2 * (5 + 49)
S = 6 * 54
S = 324.
Conclusion
Thus, the sum of the series 5 + 9 + 13 + ... + 49 is 324. Therefore, the correct answer is option 'C'.
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The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)435Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)435Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)435Correct answer is option 'C'. Can you explain this answer?.
The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)435Correct answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)435Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)435Correct answer is option 'C'. Can you explain this answer?.
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