Arithmetic Series 3

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9 years, 7 months ago

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joshua boddy 9 years, 7 months ago

Gave some feedback: Ready to use

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joshua boddy 9 years, 8 months ago

Created this as a copy of Arithmetic Series 2.

Name	Status	Author	Last Modified
Arithmetic Series 2	Ready to use	joshua boddy	01/06/2016 09:47
Arithmetic Series 3	Ready to use	joshua boddy	01/06/2016 09:47
Arithmetic Series 2	draft	Xiaodan Leng	11/07/2019 07:08
Arithmetic Series 3	draft	Xiaodan Leng	11/07/2019 07:09

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Question statement

In an arithmetic series, the $\var{n1}$ ^thterm is $\var{t1}$ and the $\var{n2}$ ^thterm is $\var{t2}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
d	integer	8
n1	integer	7
t1	integer	50
n2	integer	4
t2	integer	26
sqdisc	number	64016
disc	number	253.0138336139
n_val	integer	17

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Generated value: `integer`

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d
n_val
sqdisc
t1
t2

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To find the common difference d we note that the $\var{n1}$ ^th term is $\var{t1}$ and the $\var{n2}$ ^thterm is $\var{t2}$ so we can find the common difference d by noting $\var{t2}-\var{t1}=(\var{n2}-\var{n1})\times d$ , hence common difference $= \var{d}$

To find the least positive value for n for which the sum of the first terms of the series exceeds 1000, we recall that the sum of an arithmetic series can be found with the formula $S_n = \frac{n(2a_1 + (n-1)\times d)}{2}$ where $a_1$ denotes the first term and d denotes the common difference. Now we want to find the smallest positive $n$ such that $S_n > 1000$ . This is now a matter of solving a quadratic, which is left as an exercise.

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This question is used in the following exams:

My First Exam by Madonna Herron in Madonna's workspace.
Arithmetic sequence and series by Jinhua Mathias in Deactivated user's workspace.
Arithmetic Series by Gareth Woods in Gareth's workspace.

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joshua boddy 9 years, 7 months ago

joshua boddy 9 years, 8 months ago

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Arithmetic Series 3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

joshua boddy 9 years, 7 months ago

joshua boddy 9 years, 8 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`