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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?
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Verified Answer
The sum of the series 5 + 9 + 13 + … + 49 is:a)351b)535c)324d)4...
Concept:
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:
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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'.
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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?
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