Math Problem Statement
[1+4/3] [1+4/7] [1+4/11]....1+4/95
Solution
The sequence you provided appears to follow the form:
This can be described as a sequence where the terms are in the general form:
-
The denominator follows the pattern , which increases by 4 in each step, giving us the sequence of odd multiples of 4 minus 1.
-
The -th term can be expressed as:
So for , we get , for , we get , and so on, until , which gives us (since ).
Would you like further details on this sequence, such as summing the terms or exploring more properties?
Here are five related questions:
- How do you find the sum of the first 24 terms of this sequence?
- How does the sequence behave as increases?
- What is the general form for any term in sequences with similar patterns?
- Can this sequence be expressed as a function of for other values of the numerator (instead of 4)?
- How do you approach sequences with more complex patterns in the denominator?
Tip: Always look for patterns in the denominators of fractions in sequences; this helps in finding the general term.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Sequences
Arithmetic Progression
Rational Expressions
Formulas
a_n = 1 + 4/(4n - 1)
Theorems
General Formula for Arithmetic Progression
Suitable Grade Level
Grades 9-12
Related Recommendation
Finding the Next Term in a Fraction Sequence 1/24, 1/20, 1/16, 1/12
Understanding Mixed Sequences: Arithmetic and Geometric Progressions
Calculate First Three Terms and Formula for Sequence an = (1 - 1/4) (1 - 1/9) ...
Find the nth Term of Sequences with Fractions and Alternating Signs
Formula and First 3 Terms of Product Series an = (1 - 1/n^2) for n >= 2