5. 3, 12, 48, 192, 768, ...
You can find the 15th term by using the formula [tex]a_n = a_1 *r^{n-1}[/tex], where [tex]a_1[/tex] is the first term of the sequence, r is the common ratio, and n is the number of the term you want to find.
[tex]a_n = a_1 *r^{n-1}[/tex] Plug in your information (the common ration is x4)
[tex]a_{15} = 3 * 4^{14}[/tex] Simplify the exponent
[tex]a_{15} = 3 * 268435456[/tex] Multiply
[tex]a_{15} = 805306368[/tex]
The 15th term of the sequence is 805306368.
6. 200, 40, 8, 1.6, ...
Using guess and check, I found that the pattern here is ÷5, ÷5, ÷5, .... That can also be written as ×[tex] \frac{1}{5} [/tex], ×[tex] \frac{1}{5} [/tex], ×[tex] \frac{1}{5} [/tex], ... When you are multiplying the terms of a sequence, that is a geometric sequence.
