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

Question

Question

This question was previously asked in

Kerala PSC Common Preliminary Exam (GRADUATE LEVEL) PYP 38-24

Answer 1

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