Answer:
[tex]a_{15}=-268,435,456[/tex]
Step-by-step explanation:
First, find what factor each term is multiplied by to get to the next. To do this, divide the second term by the first, the third term by the second, etc
[tex]4\div-1=-4\\-16\div4=-4\\64\div-16=-4[/tex]
The common factor is 4. Using that, you can now write the equation for the geometric sequence in the form of:
[tex]a_n=a_1x^{n-1}[/tex]
It looks scarier than it is. aₙ is the nth term in the sequence, x is the factor, and n is the index in the sequence, that's all it is.
Plug in the information we have to get the equation for this sequence:
[tex]a_n=(-1)(-4)^{n-1}[/tex]
Then, you can solve for the 15th term:
[tex]a_{15}=(-1)(-4)^{15-1}\\a_{15}=(-1)(-4)^{14}\\a_{15}=(-1)(268,435,456)\\a_{15}=-268,435,456[/tex]
Basically, just raise the scale factor to the power of the term you want minus 1, then multiply that by the first number.
