Question

Dada a sequência 100,112,124,136,148,160,172,184 calcule a soma dos termos dessa p.a ?

Answer 1

$a_{1} =100 \\ \\ a_{2} =112 \\ \\ r= a_{2} - a_{1} \\ \\ r=112-100 \\ \\ r=12 \\ \\ n=8 \\ \\ a_{8} =184$

$S_{n} = \frac{( a_{1} + a_{n}).n }{2} \\ \\ S_{8} = \frac{( a_{1} + a_{8}).8 }{2} \\ \\ S_{8} = \frac{( 100 + 184).8 }{2} \\ \\ S_{8} = \frac{284.8}{2} \\ \\ S_{8} = \frac{2272}{2} \\ \\ S_{8} =1136$

Answer 2

Ola Cintia

a1 = 100
a2 = 112

r = a2 - a1 = 112 - 100 = 12

termo geral

an = a1 + r(n - 1)

100 + 12*(n - 1) = 184

12*(n - 1) = 84

n - 1 = 84/12 = 7

n = 8 termos

soma
Sn = (a1 + an)*n/2
Sn = (100 + 184)*8/2 = 1136

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