Question

A soma dos 5 primeiro termo de uma P. A é=29 calcular a razão sabendo que o primeiro termo é=5

Answer 1

$\large A ~raz\tilde{a}o ~da ~PA ~ \Rightarrow ~ r = \dfrac{2}{5}$

                              $\Large Progress\tilde{a}o ~Aritm\acute{e}tica$

$Sn = ( a1 + an ) . n / 2\\\\ 29 = (5 + an ) .5 / 2\\\\29 ~. ~2 = (5 + an ) .5 \\\\58 = 25 + 5an\\\\58 - 25 = 5an\\\\5an = 33\\\\an = \dfrac{33}{5}$

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$an = a1 + ( n -1 ) . r \\\\an = 5 + ( 5 -1 ) . r\\\\ \dfrac{33}{5} = 5+ ( 4) . r\\\\\\ \dfrac{33}{5} = 5+ 4r\\\\\\ \dfrac{33}{5} - 5 = 4r\\\\\\ \dfrac{8}{5} = 4r\\\\\\r = \dfrac{8}{\dfrac{5}{4}}\\\\\\r = \dfrac{2}{5}$

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Prova:

razão pode ser expressa como r = 0,4

$Sn = ( a1 + an ) . n / 2\\\\ S5 = ( 5 + 6,6 ) . 5 / 2 \\\\ S5 = 11,6 . 2,5\\\\ S5 = 29$

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