Math Problem Statement
The general term of a sequence is given as tn = n∑ i=1 i. (a) Give the first four terms of the sequence
Solution
The general term of the sequence is given as:
This means that for each , is the sum of the first natural numbers.
To find the first four terms of the sequence, we'll calculate:
So, the first four terms of the sequence are:
Would you like further clarification on this or more details? Here are some related questions to explore:
- What is the general formula for the sum of the first natural numbers?
- How does this sequence relate to triangular numbers?
- Can you express the -th term using a closed-form formula instead of a summation?
- What is the 10th term of the sequence?
- How can this type of sequence be represented graphically?
Tip: The sum of the first natural numbers can be found using the formula .
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Math Problem Analysis
Mathematical Concepts
Sequences and Series
Summation
Natural Numbers
Triangular Numbers
Formulas
Sum of first n natural numbers: n(n + 1) / 2
Theorems
Triangular Number Theorem
Suitable Grade Level
Grades 6-8