Answer:
4.
5th term = -(2/25 x -5) = 2/125
6th term = -2/(125 x - 5) = -2/625
7th term = 2/(625 x-5) = 2/3125
5.
[tex]a_k = 10 (\frac{-1}{5} )^{k-1}[/tex]
6 .
[tex]a_{12} = 10 (-\frac{1}{5} ) ^ {11} = -\frac{10}{48828125}[/tex]
Step-by-step explanation:
This is a geometric sequence with the common ratio 1/5 and sign that changes every alternate term. We can also state that the common ratio is - [tex]\frac{1}{5}[/tex]
First term is 10 with +ve sign
Second term is 10/5 with negative sign = -2
Third term is -2/5 with positive sign = 2/5
Fourth term is 2/5 ÷ 5 = 2/25 with negative sign = -2/25
4. Since each subsequent term = (-1/5) x (previous term) we have
5th term = -(2/25 x -5) = 2/125
6th term = -2/(125 x - 5) = -2/625
7th term = 2/(625 x-5) = 2/3125
5. General equation
Let [tex]a_k[/tex] be the kth term
Since this is a geometric sequence, the general equation is
[tex]a_k = a_1r^{k-1}[/tex]
[tex]\text{where } a_1 \text { is the first term and r is the common ratio}[/tex]
so the equation is
[tex]a_k = 10 (\frac{-1}{5} )^{k-1}[/tex]
6. The 12 term is calculated as
[tex]a_{12} = 10 (-\frac{1}{5} ) ^ {11} = -\frac{10}{48828125}[/tex]
