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The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it?
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The number of the terms of the series 10 9 2/3 9 1/3 9 .will amo...
Solution:
To find out the number of terms in the series, we need to first find out the common difference between the terms.
Step 1: Finding the common difference
We can see that the common difference between the terms is -10/3.
Step 2: Finding the nth term of the series
The nth term of the series can be calculated using the formula:
an = a1 + (n-1)d
where
an = nth term
a1 = first term
d = common difference
Substituting the values in the formula, we get:
an = 10 + (n-1) (-10/3)
an = 10 - (10/3)(n-1)
an = (30 - 10n + 10)/3
an = (40 - 10n)/3
Step 3: Finding the value of n
We want the sum of the series to be equal to 155. The sum of the series can be calculated using the formula:
Sn = n/2 (a1 + an)
Substituting the values, we get:
155 = n/2 (10 + (40 - 10n)/3)
310 = n(30 - 3n + 10)
310 = n(40 - 3n)
310 = 40n - 3n^2
3n^2 - 40n + 310 = 0
Solving the quadratic equation, we get:
n = 20 or n = 51.67
Since n has to be a whole number, we take n = 20.
Therefore, the number of terms in the series is 20.
To find out the number of terms in the series, we need to first find out the common difference between the terms.
Step 1: Finding the common difference
We can see that the common difference between the terms is -10/3.
Step 2: Finding the nth term of the series
The nth term of the series can be calculated using the formula:
an = a1 + (n-1)d
where
an = nth term
a1 = first term
d = common difference
Substituting the values in the formula, we get:
an = 10 + (n-1) (-10/3)
an = 10 - (10/3)(n-1)
an = (30 - 10n + 10)/3
an = (40 - 10n)/3
Step 3: Finding the value of n
We want the sum of the series to be equal to 155. The sum of the series can be calculated using the formula:
Sn = n/2 (a1 + an)
Substituting the values, we get:
155 = n/2 (10 + (40 - 10n)/3)
310 = n(30 - 3n + 10)
310 = n(40 - 3n)
310 = 40n - 3n^2
3n^2 - 40n + 310 = 0
Solving the quadratic equation, we get:
n = 20 or n = 51.67
Since n has to be a whole number, we take n = 20.
Therefore, the number of terms in the series is 20.
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The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it?
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The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it?.
The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of the terms of the series 10 9 2/3 9 1/3 9 .will amount to 155 is ? please explain it?.
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