Given that a sequence has a1=3

and r=0.2

1 answer

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!