Evan's copy of Arithmetic Series 4

Error

There was an error loading the page.

Contributors

Evan Weinberg

History

○

Evan Weinberg 8 years, 6 months ago

Created this as a copy of Arithmetic Series 4.

Name	Status	Author	Last Modified
Arithmetic Series 4	Ready to use	joshua boddy	01/06/2016 09:47
Jinhua's copy of Arithmetic Series 4	Ready to use	Jinhua Mathias	28/08/2024 12:15
Evan's copy of Arithmetic Series 4	draft	Evan Weinberg	24/08/2016 02:34
Sequences 3	draft	Mark Hodds	06/11/2016 20:42
Arithmetic Series 4	draft	Xiaodan Leng	11/07/2019 05:32
Arithmetic Series 4	draft	Xiaodan Leng	11/07/2019 07:05

There are 6 other versions that do you not have access to.

Question statement

The $\var{n}$ ^thterm of an arithmetic series is $\simplify{{t1}+({n}-1)*{d}}$

The common difference is $\var{d}$

Give any introductory information the student needs.

			Name	Type	Generated Value

t1	integer	2
d	integer	7
t2	integer	9
t3	integer	16
t4	integer	23
tr	integer	7
tsum	integer	16
tans	rational	872
n	integer	9

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..9)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

d
t2
t3
t4
tans

This variable doesn't seem to be used anywhere.

Advice

To find the firstterm, we note that the $\var{n}$ ^th term is $\simplify{{t1}+({n}-1)*{d}}$ and the common difference is $\var{d}$ hence we can calculate the first term as $\simplify{{t1}+({n}-1)*{d}}-(\var{n}-1)\times\var{d}$

To find the sum of the first $\var{tsum}$ terms we used the known formula $S_n = \frac{n(a_1 + a_n)}{2}$ where $a_i$ is the $i$ ^th term of the arithmetic series. Since we know how to calculate $a_n$ from our above considerations, we know that $S_n = \frac{n(a_1+a_1+(n-1)\times d)}{2}$ which simplifies to $S_n = \frac{n(2\times\var{t1}+(n-1)\var{d})}{2}$

Answers: 1st term is {t1}, sum is {tans}

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exam:

Standard 1.2-1.3 Arithmetic & Geometric Series, Sigma Notation (IB) by Evan Weinberg in Evan's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Evan Weinberg 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Number entry

Advanced settings

Loading...

Error

Evan's copy of Arithmetic Series 4

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Evan Weinberg 8 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`