Progresiones aritméticas: Ecuaciones simultaneas

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Luis Hernandez 6 years, 3 months ago

Created this as a copy of Hallar la diferencia y el primer término de una progresión....

Name	Status	Author	Last Modified
Hallar la diferencia y el primer término de una progresión...	Ready to use	Luis Hernandez	02/12/2020 15:42
Progresiones aritméticas: Ecuaciones simultaneas	draft	Luis Hernandez	02/12/2020 15:42

Question statement

La suma de los primeros términos \ (\ var {n1} \) de una progresión aritmética es \ (\ var {s1} \) y el término \ (\ var {n2} th \) de la misma serie es \ (\ var {T} \).

Give any introductory information the student needs.

			Name	Type	Generated Value

n1	integer	5
s1	integer	44
n2	integer	13
T	integer	11
d	rational	11/50
a	rational	209/25

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap This gap is not used in the parent part's prompt. Gap 0. Number entry
  Add
2. Gap This gap is not used in the parent part's prompt. Gap 1. Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Calcula el valor de la diferencia común. \ (d \) = Gap NaN

Calcula el valor del primer término de la serie. \ (a \) = Gap NaN

Advice

Recall the formula for the sum of the first n terms of an arithmetic progression is $S_n=\frac{n}{2}(2a+(n-1)d)$ .

The sum of the first $\var{n1}$ terms of an arithmetic progression is $\var{s1}$

$\frac{\var{n1}}{2}(2a+\simplify{{n1}-1}d)=\var{s1}$ equation (i)

The formula for nth term of an arithmetic progression is $T_n=a+(n-1)d$ .

The $\var{n2}th$ term of the same series is $\var{T}$

$a+\simplify{{n2}-1}d=\var{T}$ equation (ii)

Here we have two simultaneous equations. We can eliminate the $a$ term.

$\var{n1}a+\simplify{({n1}-1)*{n1}/2}d=\var{s1}$ equation (i)

$\var{n1}a+\simplify{{n1}*({n2}-1)}d=\simplify{{n1}*{T}}$ equation (ii)* $\var{n1}$

$\simplify{({n1}-1)*{n1}/2-{n1}*({n2}-1)}d=\simplify{{s1}-{n1}*{T}}$

$d=\frac{\simplify{{s1}-{n1}*{T}}}{\simplify{({n1}-1)*{n1}/2-{n1}*({n2}-1)}}$

$d=\simplify{({s1}-{n1}*{T})/(({n1}-1)*{n1}/2-{n1}*({n2}-1))}$

Using this result and equation (ii) we can find the value for $a$

$a+\simplify{({n2}-1)*({s1}-{n1}*{T})/(({n1}-1)*{n1}/2-{n1}*({n2}-1))}=\var{T}$

$a=\var{T}-\simplify{({n2}-1)*({s1}-{n1}*{T})/(({n1}-1)*{n1}/2-{n1}*({n2}-1))}$

$a=\simplify{{T}-({n2}-1)*({s1}-{n1}*{T})/(({n1}-1)*{n1}/2-{n1}*({n2}-1))}$

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Progresiones aritméticas: Ecuaciones simultaneas

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Error

Progresiones aritméticas: Ecuaciones simultaneas

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`