How many terms will have to be added to get a sum of 10877 in the arithmetic series? 5, 9, 13,...

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Kerala PSC Common Preliminary Exam (GRADUATE LEVEL) PYP 38-24
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  1. 71 
  2. 63 
  3.  73 
  4. 74 

Answer (Detailed Solution Below)

Option 3 :  73 
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Detailed Solution

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Ans: (C) 73 
Key Points : 
To find the number of terms n in the arithmetic series 5,9,13,… that sum to 10877:
The sum of an arithmetic series is:
Sn=n/2[2a+(n−1)d]
Here, Sn=10877, a=5, d=4.
 Substitute the values:
10877=n/2[10+4(n−1)]
Simplify:
10877=n/2(4n+6)
10877=2n2+3n
Solve 2n2+3n−10877=0
n=−[3±√32−4(2)(−10877)] / 2(2)
n=[−3±295] / 4
n=4−3+295​=73
Additional Information :
  • Formula for Sum of Arithmetic Series: The sum (Sn) of an arithmetic series is given by the formula: Sn = (n/2) * [2a + (n-1)d], where 'n' is the number of terms, 'a' is the first term, and 'd' is the common difference.
  • Given Values: In this problem, we are given:
  • Sn = 10877 (the sum of the series)
  • a = 5 (the first term)
  • d = 4 (the common difference)
  • Substitution: Substitute the given values into the formula: 10877 = (n/2) * [2*5 + (n-1)*4]
  • Simplification: Simplify the equation: 10877 = (n/2) * [10 + 4n - 4] 10877 = (n/2) * (4n + 6) 10877 = n * (2n + 3) 10877 = 2n² + 3n

 

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