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The sum of the series 9 ,5,1,.to 100 terms is?
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The sum of the series 9 ,5,1,.to 100 terms is?
Calculating the Sum of an Arithmetic Series
An arithmetic series is a sequence of numbers with a constant difference between consecutive terms. The formula to calculate the sum of an arithmetic series is:
S_n = n/2 [2a + (n-1)d]
where S_n is the sum of the first n terms of the series, a is the first term, d is the common difference between terms, and n is the number of terms in the series.
Applying the Formula to the Given Series
In the given series, the first term (a) is 9, the common difference (d) is -4 (since each term is 4 less than the previous one), and the number of terms (n) is 100.
Substituting these values into the formula:
S_100 = 100/2 [2(9) + (100-1)(-4)]
S_100 = 50 [18 - 396]
S_100 = -18,900
Therefore, the sum of the series is -18,900.
An arithmetic series is a sequence of numbers with a constant difference between consecutive terms. The formula to calculate the sum of an arithmetic series is:
S_n = n/2 [2a + (n-1)d]
where S_n is the sum of the first n terms of the series, a is the first term, d is the common difference between terms, and n is the number of terms in the series.
Applying the Formula to the Given Series
In the given series, the first term (a) is 9, the common difference (d) is -4 (since each term is 4 less than the previous one), and the number of terms (n) is 100.
Substituting these values into the formula:
S_100 = 100/2 [2(9) + (100-1)(-4)]
S_100 = 50 [18 - 396]
S_100 = -18,900
Therefore, the sum of the series is -18,900.
Community Answer
The sum of the series 9 ,5,1,.to 100 terms is?
N = 100
a = 9
d = -4
so Sum = Sn = n / 2 *(a + an)
an = nth term = a+(n-1)d
= 9 + (100-1) (-4)
= 9 - 396
= -387
so Sum = 100/2 [9 + (-387)]
= 50 * (-378)
= - 18900
a = 9
d = -4
so Sum = Sn = n / 2 *(a + an)
an = nth term = a+(n-1)d
= 9 + (100-1) (-4)
= 9 - 396
= -387
so Sum = 100/2 [9 + (-387)]
= 50 * (-378)
= - 18900
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The sum of the series 9 ,5,1,.to 100 terms is?
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The sum of the series 9 ,5,1,.to 100 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 9 ,5,1,.to 100 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 9 ,5,1,.to 100 terms is?.
The sum of the series 9 ,5,1,.to 100 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 9 ,5,1,.to 100 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 9 ,5,1,.to 100 terms is?.
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