Question

помните пожалуйста срочно! Алгебра 9 класс​

Answer 1

$1)\; \; a_4=5\; \; ,\; \; a_7=320\\\\a_4=a_1q^3=5\; \; ,\; \; a_7=a_1q^6=320\\\\a_1=\frac{5}{q^3}\; \; ,\; \; a_1=\frac{320}{q^6}\\\\\frac{5}{q^3}=\frac{320}{q^6}\; \; \to \; \; \; \frac{q^6}{q^3}=\frac{320}{5}\; \; ,\; \; q^3=64\; ,\; \; \boxed {q=4}$

$2)\; \; a_1=-2\; \; ,\; \; q=-\frac{1}{2}\\\\S_5=\frac{a_1(q^5-1)}{q-1}=\frac{-2(-\frac{1}{32}-1)}{-\frac{1}{2}-1}=\frac{-2\cdot (-\frac{33}{32})}{-\frac{3}{2}}=-\frac{2\cdot 33\cdot 2}{32\cdot 3}=-\frac{11}{8}=-1\frac{3}{8}$

$3)\; \; a_1=-\frac{1}{36}\; \; ,\; \; q=-2\\\\S_{10}=\frac{a_1(q^{10}-1)}{q-1}=\frac{-1\cdot (1024-1)}{36\cdot (-2-1)}=\frac{1023}{36\cdot 3}=\frac{341}{36}=9\frac{17}{36}$

$4)\; \; a_1=48\; \; ,\; \; q=-\frac{1}{2}\\\\S_6=\frac{a_1(q^6-1)}{q-1}=\frac{48(\frac{1}{64}-1)}{-\frac{1}{2}-1}=\frac{48\cdot (-\frac{63}{64})}{-\frac{3}{2}}=\frac{4\cdot 63\cdot 2}{3\cdot 64}=\frac{21}{8}=2,625$

$5)\; \;a_{n}=15\; \; ,\; \; a_{1}=240\; \; ,\; \; q=0,5\\\\a_{n}=a_1q^{n-1}\; \; \to \; \; 15=240\cdot (0,5)^{n-1}\; \; ,\; \; (0,5)^{n-1}=\frac{1}{16}\; ,\\\\(\frac{1}{2})^{n-1}=(\frac{1}{2})^4\; \; \; \to \; \; n-1=4\; \; ,\; \; n=1+4\; \; ,\; \; \boxed {n=5}$