Mathematics: 2, -10, 50 what is the next term in the sequence

2, -10, 50 what is the next term in the sequence

neariah24

26.01.2022

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Step-by-step explanation:

$2,\:-10,\:50$

$\mathrm{Check\:whether\:the\:ratio\:is\:constant}:\quad r=-5$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{-10}{2}=-5,\:\quad \frac{50}{-10}=-5$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

r=-5

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

a_1=2

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}$

$r=-5,\:a_n=2\left(-5\right)^{n-1}$

$\mathrm{The\:next\:term\:is}$

$\mathrm{Let\:}n=4$

$a_4=2\left(-5\right)^{4-1}$

$2\left(-5\right)^{4-1}=-250$

a_4=-250

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