Question
upstudy study bank question image url

3.1 The term of an arithmetic sequence is -3 and the term is -35 .
Determine the common difference and the first term.
3.2 Evaluate :
3.3 The following sequence forms a convergent geometric sequence:

Determine the possible values of x .
3.3 .2 If , calculate .

Ask by Valdez Johnson. in South Africa
Jan 03,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

  • 3.1
    • First term: 3
    • Common difference: -2
  • 3.2
  • 3.3.1
  • 3.3.2

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Beyond the Answer

To find the common difference and the first term of the arithmetic sequence, you can use the formula for the -th term, . Set up two equations based on the term (-3) and the term (-35). Solving these yields and .
In the geometric sequence, to ensure convergence, the absolute value of the ratio needs to be less than 1. Here, you can analyze each term in relation to and derive to find the valid range for . This means .

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy