Question1) What is the series of the sequence $\{1,4,7,10,13\}$ ? $\square$ Check Show answer 2) What is $a_{10}$ for the sequence $\{2,6,10, \ldots\}$ ? $\square$ Check Show answer 3) What is $S_{10}$ for the sequence $\{2,6,10, \ldots\}$ ? $\square$ Check Show answer. 4) What is $\sum_{n=1}^{20} 3 n$ ? $\square$ Check Show answer

Studdy Solution
Evaluate $\sum_{n=1}^{20} 3n$. Recognize this as an arithmetic series where each term is $3n$. The sum of the first $20$ terms can be calculated as:
$$\sum_{n=1}^{20} 3n = 3 \sum_{n=1}^{20} n$$
The sum of the first $n$ natural numbers is $\frac{n(n+1)}{2}$, so:
$$\sum_{n=1}^{20} n = \frac{20 \times 21}{2} = 210$$
Thus:
$$\sum_{n=1}^{20} 3n = 3 \times 210 = 630$$
The solutions are: 1) Series: $a_n = 1 + (n-1) \times 3$ 2) $a_{10} = 38$ 3) $S_{10} = 200$ 4) $\sum_{n=1}^{20} 3n = 630$