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jasmine8142002
27.06.2019 •
Mathematics
Find sn for the arithmetic series 5+7+9 + … and determine the value of n for which the series has sum 165.
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Ответ:
The sum of n terms for the arithmetic series is:
The value of n for which the series has sum 165 is 11
The given series is:
5 + 7 + 9 +.......
The first value, a = 5
The common difference, d = 7 - 5
d = 2
The sum of the first n terms of an arithmetic series is given by the formula:
Substituting a = 5, and d = 2 into the sum of the series, we have:
To determine the value of n for which the series has sum 165, substitute
into the sum above
The value of n for which the series has sum 165 is 11
Learn more on Arithmetic Progression here: link
Ответ:
see explanation
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
where d is the common difference and a is the first term
here d = 9 - 7 = 7 - 5 = 2 and a = 5, hence
=
(10 + 2n - 2)
=
(2n + 8)
= n² + 4n
When sum = 165, then
n² + 4n = 165 ← rearrange into standard form
n² + 4n - 165 = 0 ← in standard form
(n + 15)(n - 11) = 0 ← in factored form
equate each factor to zero and solve for n
n + 15 = 0 ⇒ n = - 15
n - 11 = 0 ⇒ n = 11
but n > 0 ⇒ n = 11
Ответ:
D. $152