The general term of a sequence is given as
tn =
n∑
i=1
i.
(a) Give the first four terms of the sequence

The general term of the sequence is given as:

\[
t_n = \sum_{i=1}^{n} i
\]

This means that for each \( n \), \( t_n \) is the sum of the first \( n \) natural numbers.

To find the first four terms of the sequence, we'll calculate:

1. \( t_1 = \sum_{i=1}^{1} i = 1 \)
2. \( t_2 = \sum_{i=1}^{2} i = 1 + 2 = 3 \)
3. \( t_3 = \sum_{i=1}^{3} i = 1 + 2 + 3 = 6 \)
4. \( t_4 = \sum_{i=1}^{4} i = 1 + 2 + 3 + 4 = 10 \)

So, the first four terms of the sequence are:

\[
t_1 = 1, \quad t_2 = 3, \quad t_3 = 6, \quad t_4 = 10
\]

Would you like further clarification on this or more details? Here are some related questions to explore:

1. What is the general formula for the sum of the first \( n \) natural numbers?
2. How does this sequence relate to triangular numbers?
3. Can you express the \( n \)-th term using a closed-form formula instead of a summation?
4. What is the 10th term of the sequence?
5. How can this type of sequence be represented graphically?

**Tip:** The sum of the first \( n \) natural numbers can be found using the formula \( \frac{n(n+1)}{2} \).

The general term of a sequence is given as tn = sum(i=1 to n) i. (a) Give the first four terms of the sequence.

Learn how to find the first four terms of a sequence where the general term is given by tn = sum(i=1 to n) i. Explore key mathematical concepts such as summation and triangular numbers with detailed step-by-step explanations. Suitable for students in Grades 6-8.

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