Subjects algebra

Sequence Terms 5A2173

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We have a sequence defined by the formula $a_n = \frac{n + 2}{4n}$ for any natural number $n$. We need to find the first three terms of this sequence. 2. **Formula used:** The general term of the sequence is given by $$a_n = \frac{n + 2}{4n}$$ where $n$ is a natural number (i.e., $n = 1, 2, 3, \ldots$). 3. **Calculate the first term ($n=1$):** $$a_1 = \frac{1 + 2}{4 \times 1} = \frac{3}{4}$$ 4. **Calculate the second term ($n=2$):** $$a_2 = \frac{2 + 2}{4 \times 2} = \frac{4}{8} = \frac{1}{2}$$ 5. **Calculate the third term ($n=3$):** $$a_3 = \frac{3 + 2}{4 \times 3} = \frac{5}{12}$$ 6. **Final answer:** The first three terms of the sequence are $$\frac{3}{4}, \frac{1}{2}, \frac{5}{12}$$ These values represent the sequence terms for $n=1, 2, 3$ respectively.