Arithmetic Sequence - find the biggest value [on hold]
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If $x$, $y$, $z$ and $t$ form an arithmetic sequence and $x + y + z + t = 26$ and $xt/yz=11/20$, then which one of $x$, $y$, $z$ or $t$ will be having the biggest value?
sequences-and-series
edited Nov 12 at 10:50
Rócherz
2,4362619
asked Nov 12 at 9:14
Sean Goudarzi
1285
put on hold as off-topic by Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz Nov 13 at 12:38
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
If $x$, $y$, $z$ and $t$ form an arithmetic sequence and $x + y + z + t = 26$ and $xt/yz=11/20$, then which one of $x$, $y$, $z$ or $t$ will be having the biggest value?
sequences-and-series
edited Nov 12 at 10:50
Rócherz
2,4362619
asked Nov 12 at 9:14
Sean Goudarzi
1285
put on hold as off-topic by Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz Nov 13 at 12:38
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz
If this question can be reworded to fit the rules in the help center, please edit the question.
2
What did you try?
– Parcly Taxel
Nov 12 at 9:17
Approach the problem with the definition of an arithmetic sequence. The first number is $x$, the second number is $x+a = y$ for some $a$, etc.
– Matti P.
Nov 12 at 9:19
2
Since both equations are symmetric in $x,t$ (i.e. you can exchange the values of $x$ and $t$ without affecting the equations) and also symmetric in $y,z$, it is impossible to tell which term in greatest from the information given. At best you can conclude that one of $x$ and $t$ has the greatest value.
– gandalf61
Nov 12 at 9:46
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If $x$, $y$, $z$ and $t$ form an arithmetic sequence and $x + y + z + t = 26$ and $xt/yz=11/20$, then which one of $x$, $y$, $z$ or $t$ will be having the biggest value?
sequences-and-series
edited Nov 12 at 10:50
Rócherz
2,4362619
asked Nov 12 at 9:14
Sean Goudarzi
1285
If $x$, $y$, $z$ and $t$ form an arithmetic sequence and $x + y + z + t = 26$ and $xt/yz=11/20$, then which one of $x$, $y$, $z$ or $t$ will be having the biggest value?
sequences-and-series
sequences-and-series
edited Nov 12 at 10:50
Rócherz
2,4362619
asked Nov 12 at 9:14
Sean Goudarzi
1285
edited Nov 12 at 10:50
Rócherz
2,4362619
asked Nov 12 at 9:14
Sean Goudarzi
1285
edited Nov 12 at 10:50
Rócherz
2,4362619
edited Nov 12 at 10:50
Rócherz
2,4362619
edited Nov 12 at 10:50
Rócherz
2,4362619
2,4362619
asked Nov 12 at 9:14
Sean Goudarzi
1285
asked Nov 12 at 9:14
Sean Goudarzi
1285
asked Nov 12 at 9:14
Sean Goudarzi
1285
1285
put on hold as off-topic by Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz Nov 13 at 12:38
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz Nov 13 at 12:38
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Nosrati, Shailesh, ArsenBerk, ancientmathematician, A. Pongrácz
If this question can be reworded to fit the rules in the help center, please edit the question.
2
What did you try?
– Parcly Taxel
Nov 12 at 9:17
Approach the problem with the definition of an arithmetic sequence. The first number is $x$, the second number is $x+a = y$ for some $a$, etc.
– Matti P.
Nov 12 at 9:19
2
Since both equations are symmetric in $x,t$ (i.e. you can exchange the values of $x$ and $t$ without affecting the equations) and also symmetric in $y,z$, it is impossible to tell which term in greatest from the information given. At best you can conclude that one of $x$ and $t$ has the greatest value.
– gandalf61
Nov 12 at 9:46
add a comment |
2
What did you try?
– Parcly Taxel
Nov 12 at 9:17
Approach the problem with the definition of an arithmetic sequence. The first number is $x$, the second number is $x+a = y$ for some $a$, etc.
– Matti P.
Nov 12 at 9:19
2
Since both equations are symmetric in $x,t$ (i.e. you can exchange the values of $x$ and $t$ without affecting the equations) and also symmetric in $y,z$, it is impossible to tell which term in greatest from the information given. At best you can conclude that one of $x$ and $t$ has the greatest value.
– gandalf61
Nov 12 at 9:46
2
2
What did you try?
– Parcly Taxel
Nov 12 at 9:17
What did you try?
– Parcly Taxel
Nov 12 at 9:17
Approach the problem with the definition of an arithmetic sequence. The first number is $x$, the second number is $x+a = y$ for some $a$, etc.
– Matti P.
Nov 12 at 9:19
Approach the problem with the definition of an arithmetic sequence. The first number is $x$, the second number is $x+a = y$ for some $a$, etc.
– Matti P.
Nov 12 at 9:19
2
2
Since both equations are symmetric in $x,t$ (i.e. you can exchange the values of $x$ and $t$ without affecting the equations) and also symmetric in $y,z$, it is impossible to tell which term in greatest from the information given. At best you can conclude that one of $x$ and $t$ has the greatest value.
– gandalf61
Nov 12 at 9:46
Since both equations are symmetric in $x,t$ (i.e. you can exchange the values of $x$ and $t$ without affecting the equations) and also symmetric in $y,z$, it is impossible to tell which term in greatest from the information given. At best you can conclude that one of $x$ and $t$ has the greatest value.
– gandalf61
Nov 12 at 9:46
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Let the terms be $x,x+d,x+2d,x+3d$. Then:
$$begin{cases}4x+6d=26\ frac{x(x+3d)}{(x+d)(x+2d)}=frac{11}{20}end{cases} Rightarrow begin{cases}x=frac{13-3d}{2} \ 9x^2+27xd-22d^2=0end{cases} Rightarrow begin{cases}x_1=2;x_2=11 \ d_1=3; d_2=-3end{cases} Rightarrow \
AP1: 2,5,8,11.\
AP2: 11,8,5,2.$$
answered Nov 12 at 16:53
bilgamish
934
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Let the terms be $x,x+d,x+2d,x+3d$. Then:
$$begin{cases}4x+6d=26\ frac{x(x+3d)}{(x+d)(x+2d)}=frac{11}{20}end{cases} Rightarrow begin{cases}x=frac{13-3d}{2} \ 9x^2+27xd-22d^2=0end{cases} Rightarrow begin{cases}x_1=2;x_2=11 \ d_1=3; d_2=-3end{cases} Rightarrow \
AP1: 2,5,8,11.\
AP2: 11,8,5,2.$$
answered Nov 12 at 16:53
bilgamish
934
add a comment |
up vote
1
down vote
accepted
Let the terms be $x,x+d,x+2d,x+3d$. Then:
$$begin{cases}4x+6d=26\ frac{x(x+3d)}{(x+d)(x+2d)}=frac{11}{20}end{cases} Rightarrow begin{cases}x=frac{13-3d}{2} \ 9x^2+27xd-22d^2=0end{cases} Rightarrow begin{cases}x_1=2;x_2=11 \ d_1=3; d_2=-3end{cases} Rightarrow \
AP1: 2,5,8,11.\
AP2: 11,8,5,2.$$
answered Nov 12 at 16:53
bilgamish
934
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Let the terms be $x,x+d,x+2d,x+3d$. Then:
$$begin{cases}4x+6d=26\ frac{x(x+3d)}{(x+d)(x+2d)}=frac{11}{20}end{cases} Rightarrow begin{cases}x=frac{13-3d}{2} \ 9x^2+27xd-22d^2=0end{cases} Rightarrow begin{cases}x_1=2;x_2=11 \ d_1=3; d_2=-3end{cases} Rightarrow \
AP1: 2,5,8,11.\
AP2: 11,8,5,2.$$
answered Nov 12 at 16:53
bilgamish
934
Let the terms be $x,x+d,x+2d,x+3d$. Then:
$$begin{cases}4x+6d=26\ frac{x(x+3d)}{(x+d)(x+2d)}=frac{11}{20}end{cases} Rightarrow begin{cases}x=frac{13-3d}{2} \ 9x^2+27xd-22d^2=0end{cases} Rightarrow begin{cases}x_1=2;x_2=11 \ d_1=3; d_2=-3end{cases} Rightarrow \
AP1: 2,5,8,11.\
AP2: 11,8,5,2.$$
answered Nov 12 at 16:53
bilgamish
934
answered Nov 12 at 16:53
bilgamish
934
answered Nov 12 at 16:53
bilgamish
934
answered Nov 12 at 16:53
bilgamish
934
934
add a comment |
add a comment |
2
What did you try?
– Parcly Taxel
Nov 12 at 9:17
Approach the problem with the definition of an arithmetic sequence. The first number is $x$, the second number is $x+a = y$ for some $a$, etc.
– Matti P.
Nov 12 at 9:19
2
Since both equations are symmetric in $x,t$ (i.e. you can exchange the values of $x$ and $t$ without affecting the equations) and also symmetric in $y,z$, it is impossible to tell which term in greatest from the information given. At best you can conclude that one of $x$ and $t$ has the greatest value.
– gandalf61
Nov 12 at 9:46