Question

Qual a soma dos termos da PA(83, 80, ..., 32)?

1139
901
885
115
131

Answer 1

$> resolucao \\ \\ \geqslant progressao \: aritmetica \\ \\ r = a2 - a1 \\ r = 80 - 83 \\ r = - 3 \\ \\ an = a1 + (n - 1)r \\ 32 = 83 + (n - 1) - 3 \\ 32 = 83 + ( - 3n) + 3 \\ 32 = 86 + ( - 3n) \\ 32 - 86 = - 3n \\ - 54 = - 3n \\ n = \frac{ - 54}{ - 3} \\ n = 18 \\ \\ \\ \geqslant \: soma \: dos \: termos \: da \: pa \\ \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{(83 + 32)18}{2} \\ \\ sn = \frac{115 \times 18}{2} \\ \\ sn = 115 \times 9 \\ \\ sn = 1035 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant \geqslant \geqslant$

Answer 2

Explicação passo a passo:

Na PA temos :

a1 = 83

a2 =80

r = 80 - 83 = - 3

an = 32

an = a1 + ( n - 1 ).r

32 = 83 + ( n - 1). -3

32 = 83 - 3n + 3

32 = 86 - 3n

32 - 86 = - 3n

-3n = - 54 ( -1 )

3n = 54

n = 54/3 = 18 >>>>

Sn = ( a1 + an ).n/2

Sn = ( 83 + 32).n/2

S18 = 115 * 18/2

S18 = 115 * 9

S18 =1035 >>>>> resposta