Finding the common difference and hence, the sum of an A.P
Find the sum to $25$ terms of an A.P with the first four terms as $1, log_yx, log_zy,-15log_x z$.
My attempt:
I started out with,
$2log_yx = 1+log_zy$
and,
$2log_zy = log_yx -15log_xz$
Further simplifying the equations led me nowhere. The work was getting too tedious. And since the exam in which I was supposed to solve this question only gives exactly 180 sec to solve this problem, I thought there might be some other, smarter way.
Any help would be appreciated.
sequences-and-series arithmetic-progressions
asked yesterday
Sahil Baori
183
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
Find the sum to $25$ terms of an A.P with the first four terms as $1, log_yx, log_zy,-15log_x z$.
My attempt:
I started out with,
$2log_yx = 1+log_zy$
and,
$2log_zy = log_yx -15log_xz$
Further simplifying the equations led me nowhere. The work was getting too tedious. And since the exam in which I was supposed to solve this question only gives exactly 180 sec to solve this problem, I thought there might be some other, smarter way.
Any help would be appreciated.
sequences-and-series arithmetic-progressions
asked yesterday
Sahil Baori
183
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
math.stackexchange.com/questions/3060501/…
– lab bhattacharjee
yesterday
add a comment |
Find the sum to $25$ terms of an A.P with the first four terms as $1, log_yx, log_zy,-15log_x z$.
My attempt:
I started out with,
$2log_yx = 1+log_zy$
and,
$2log_zy = log_yx -15log_xz$
Further simplifying the equations led me nowhere. The work was getting too tedious. And since the exam in which I was supposed to solve this question only gives exactly 180 sec to solve this problem, I thought there might be some other, smarter way.
Any help would be appreciated.
sequences-and-series arithmetic-progressions
asked yesterday
Sahil Baori
183
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Find the sum to $25$ terms of an A.P with the first four terms as $1, log_yx, log_zy,-15log_x z$.
My attempt:
I started out with,
$2log_yx = 1+log_zy$
and,
$2log_zy = log_yx -15log_xz$
Further simplifying the equations led me nowhere. The work was getting too tedious. And since the exam in which I was supposed to solve this question only gives exactly 180 sec to solve this problem, I thought there might be some other, smarter way.
Any help would be appreciated.
sequences-and-series arithmetic-progressions
sequences-and-series arithmetic-progressions
asked yesterday
Sahil Baori
183
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Sahil Baori
183
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Sahil Baori
183
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Sahil Baori
183
asked yesterday
Sahil Baori
183
183
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Sahil Baori is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
math.stackexchange.com/questions/3060501/…
– lab bhattacharjee
yesterday
add a comment |
1
math.stackexchange.com/questions/3060501/…
– lab bhattacharjee
yesterday
1
1
math.stackexchange.com/questions/3060501/…
– lab bhattacharjee
yesterday
math.stackexchange.com/questions/3060501/…
– lab bhattacharjee
yesterday
add a comment |
1 Answer
1
active
oldest
votes
Hint: we have $$frac{ln(x)}{ln(y)}=1+d$$ and $$frac{ln(y)}{ln(z)}=1+2d$$ and $$frac{ln(z)}{ln(x)}=frac{1+2d}{-15}$$ then we get
$$frac{(1+2d)(1+3d)}{-15}=frac{ln(y)}{ln(x)}=frac{1}{1+d}$$ so we obtain
$$(1+2d)(1+3d)(1+d)=-15$$
Can you solve this equation?
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sahil Baori is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3060555%2ffinding-the-common-difference-and-hence-the-sum-of-an-a-p%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hint: we have $$frac{ln(x)}{ln(y)}=1+d$$ and $$frac{ln(y)}{ln(z)}=1+2d$$ and $$frac{ln(z)}{ln(x)}=frac{1+2d}{-15}$$ then we get
$$frac{(1+2d)(1+3d)}{-15}=frac{ln(y)}{ln(x)}=frac{1}{1+d}$$ so we obtain
$$(1+2d)(1+3d)(1+d)=-15$$
Can you solve this equation?
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
add a comment |
Hint: we have $$frac{ln(x)}{ln(y)}=1+d$$ and $$frac{ln(y)}{ln(z)}=1+2d$$ and $$frac{ln(z)}{ln(x)}=frac{1+2d}{-15}$$ then we get
$$frac{(1+2d)(1+3d)}{-15}=frac{ln(y)}{ln(x)}=frac{1}{1+d}$$ so we obtain
$$(1+2d)(1+3d)(1+d)=-15$$
Can you solve this equation?
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
add a comment |
Hint: we have $$frac{ln(x)}{ln(y)}=1+d$$ and $$frac{ln(y)}{ln(z)}=1+2d$$ and $$frac{ln(z)}{ln(x)}=frac{1+2d}{-15}$$ then we get
$$frac{(1+2d)(1+3d)}{-15}=frac{ln(y)}{ln(x)}=frac{1}{1+d}$$ so we obtain
$$(1+2d)(1+3d)(1+d)=-15$$
Can you solve this equation?
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
Hint: we have $$frac{ln(x)}{ln(y)}=1+d$$ and $$frac{ln(y)}{ln(z)}=1+2d$$ and $$frac{ln(z)}{ln(x)}=frac{1+2d}{-15}$$ then we get
$$frac{(1+2d)(1+3d)}{-15}=frac{ln(y)}{ln(x)}=frac{1}{1+d}$$ so we obtain
$$(1+2d)(1+3d)(1+d)=-15$$
Can you solve this equation?
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
answered yesterday
Dr. Sonnhard Graubner
73.3k42865
73.3k42865
add a comment |
add a comment |
Sahil Baori is a new contributor. Be nice, and check out our Code of Conduct.
Sahil Baori is a new contributor. Be nice, and check out our Code of Conduct.
Sahil Baori is a new contributor. Be nice, and check out our Code of Conduct.
Sahil Baori is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3060555%2ffinding-the-common-difference-and-hence-the-sum-of-an-a-p%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
math.stackexchange.com/questions/3060501/…
– lab bhattacharjee
yesterday