Question

Dada a P.A. (28,36,44,52,...) determine:
A) o oitavo termo dessa PA
B) o décimo quinto termo dessa PA
C) o vigésimo sétimo termo dessa P.A.
D) o centésimo termo dessa P.A.
URGENTEEEE

Answer 1

$\large a) ~O~ oitavo~ termo~da~ PA~ \Rightarrow ~ a8 = 84\\\\\largeb) ~O~ d\acute{e}cimo ~quinto~ termo~da~ PA~ \Rightarrow ~ a15 = 140 \\\\\largec) ~ O~ vig\acute{e}simo ~s\acute{e}timo ~termo~ da ~PA~ \Rightarrow ~a27 = 236 \\\\\larged) ~ O~ cent\acute{e}simo ~termo~da ~PA~ \Rightarrow ~a100 = 820$

Encontrar a razão da PA:

$r = a2 - a1\\\\r = 36 - 28\\\\r = 8$

Com a razão da PA e o primeiro termo, encontrar os demais termos:

$a) ~O~ oitavo~ termo~da~ PA\\\\\\an = a1 + ( n -1 ) . r \\\\a8 = 28 + ( 8 -1 ) . 8\\\\ a8 = 28 + 7 . 8\\\\ a8 = 28 + 56\\\\ a8 = 84$                   $b) ~O~ d\acute{e}cimo ~quinto~ termo~da~ PA\\\\\\an = a1 + ( n -1 ) . r\\\\a15 = 28 + ( 15 -1 ) . 8\\\\a15 = 28 + 14 . 8\\\\ a15 = 28 + 112\\\\a15 = 140$

$c) ~ O~ vig\acute{e}simo ~s\acute{e}timo ~termo~ da~PA\\\\\\an = a1 + ( n -1 ) . r\\\\ a27 = 28 + ( 27 -1 ) . 8\\\\ a27 = 28 + 26 . 8\\\\ a27 = 28 + 208\\\\ a27 = 236$       $d) ~ O~ cent\acute{e}simo ~termo~da ~PA\\\\\\an = a1 + ( n -1 ) . r \\\\a100 =28 + ( 100 -1 ) . 8 \\\\a100 = 28 + 99 . 8 \\\\a100 = 28 + 792\\\\ a100 = 820$

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