MHB Arithmetic Progression: Finding the First Term and Common Difference

AI Thread Summary
The discussion centers on solving a problem involving an arithmetic progression (AP) where the sum of the first 100 terms is 15050, and specific terms also form a geometric progression (GP). Participants are encouraged to demonstrate effort in their inquiries by showing work and using proper formatting for mathematical expressions. Emphasis is placed on the importance of effective thread titles and posting in the correct subforum to facilitate better responses. The original poster is prompted to share their attempts at solving for the first term and common difference of the AP. Overall, the thread highlights the need for clarity and effort in seeking mathematical assistance.
Crystalong876
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The sum of the first 100 terms of an arithmetic progression is 15050; the first, third and eleventh terms of this progression are three consecutive terms of a geometric progression. Find the first term, a and the non-zero common difference, d, of the arithmetic progression.
 
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Hello and welcome to MHB, Crystalong876! :D

There are several issues of which I need to make you aware:

  • Show the nature of your question in your thread title. The title of a post should be a brief and accurate description of what your question is about. Since we assume everyone needs help, usually urgently, titles such as ‘Urgent help needed’ etc. are pointless, annoying, ineffective and lazy. You should also avoid using symbols such as ? and ! excessively in a post title for reasons already given. An effectively titled post will get more views than one with a useless title. The thread title should be at least one level more specific than the forum in which you post. For example, do not title a thread in Calculus "Calculus Problem", but "Differentiation of a Function" or "Force on a Tank".
  • Show some effort. If you want help with a question we expect you to show some effort. Effort might include showing your work, learning how to typeset equations using LATEX, making your question clearer, titling threads effectively and posting in the appropriate subforum, making a genuine attempt to understand the given help before asking for more help, and learning from previously asked questions. Moderators reserve the right to close threads in cases where the member is not making a genuine effort (particularly if the member is flooding the forums with multiple questions of the same type). You also should remember that all contributors to MHB are unpaid volunteers and are under no obligation to answer a question.
  • Choose the correct subforum. The key to posting a question in the correct subforum is to consider the content of the question, not its origin. Post questions in the subforum most appropriate for their content. For example, post questions about differential equations in the Differential Equations subforum, NOT Calculus. Post questions that are pre-calculus in content in the Pre-Calculus subforum, NOT Calculus. When in doubt, report your post using the Report Post tool (a button at the lower left corner of all posts - it looks like a triangle with an exclamation mark inside it) and so ask a moderator to review your thread location. Use a different title for each new thread.
  • No double-posting. Double-posting is sending the same post to the same or several subforums. This can lead to duplication of effort. Please post your question once only and in the correct subforum. As a courtesy, if you post your problem on multiple websites, and you get a satisfactory response on a different website, indicate in your MHB thread that you got an answer elsewhere so that our helpers do not duplicate others' efforts.

So, given these rules and policies at MHB (the complete list can be found http://mathhelpboards.com/rules/), I have moved your first thread here, given it a useful title and then deleted the 3 duplicate threads. Whew! (Sweating)

With that done, can you post what you have tried so far so our helpers know where you are stuck and can best guide you?
 
Crystalong876 said:
The sum of the first 100 terms of an arithmetic progression is 15050; the first, third and eleventh terms of this progression are three consecutive terms of a geometric progression. Find the first term, a and the non-zero common difference, d, of the arithmetic progression.
Are you able to solve this equation for a:

am = a + 2d

a = ?

If not, you'll need classroom help to solve your problem...
 
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