Question

Given that a sequence has a1=3
and r=0.2

Answer 1

It looks like you're describing a geometric sequence with the first term \( a_1 = 3 \) and a common ratio \( r = 0.2 \).

In a geometric sequence, each term is found by multiplying the previous term by the common ratio. The general formula for the \( n \)-th term of a geometric sequence is given by:

\[
a_n = a_1 \cdot r^{n-1}
\]

Using this formula, we can calculate the first few terms of the sequence:

1. **First term (\( n=1 \))**:
\[
a_1 = 3
\]

2. **Second term (\( n=2 \))**:
\[
a_2 = 3 \cdot 0.2^{2-1} = 3 \cdot 0.2 = 0.6
\]

3. **Third term (\( n=3 \))**:
\[
a_3 = 3 \cdot 0.2^{3-1} = 3 \cdot 0.2^2 = 3 \cdot 0.04 = 0.12
\]

4. **Fourth term (\( n=4 \))**:
\[
a_4 = 3 \cdot 0.2^{4-1} = 3 \cdot 0.2^3 = 3 \cdot 0.008 = 0.024
\]

5. **Fifth term (\( n=5 \))**:
\[
a_5 = 3 \cdot 0.2^{5-1} = 3 \cdot 0.2^4 = 3 \cdot 0.0016 = 0.0048
\]

If you want to find a specific term or more terms, let me know!