Ile wyrazów ma podany ciąg geometryczny?
1.
16, -8, 4, …, 1/4
a_1=16
a_2=-8
a_2=a_1*q
q=\frac{a_2}{a_1}=\frac{-8}{16}=-\frac{1}{2}
a_n=a_1*q^{n-1}
\frac{1}{4}=16* (-\frac{1}{2})^{n-1}|/16
\frac{1}{4*16}=(-\frac{1}{2})^{n-1}
\frac{1}{2^2*2^4}= (-\frac{1}{2})^{n-1}
\frac{1}{2^6}=( -\frac{1}{2} )^n*\frac{1}{-\frac{1}{2}}
\frac{1}{2^6}=( -\frac{1}{2} )^n*(-2) | /(-2)
\frac{1}{2^6*(-2)}=( -\frac{1}{2} )^n
-\frac{1}{2^6*2}=( -\frac{1}{2} )^n
-\frac{1}{2^7}=( -\frac{1}{2} )^n
(-\frac{1}{2})^7=( -\frac{1}{2} )^n
n=7 |Odpowiedź