Question

determine a soma dos 25 primeiros da pá (-7,-9,-11,...)​

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: aritmetica \\ \\ r = a2 - a1 \\ r = - 9 - ( - 7) \\ r = - 9 + 7 \\ r = - 2 \\ \\ \geqslant \: o \: 25 \: termo \: da \: pa \\ \\ an = a1 + (n - 1)r \\ an = - 7 + (25 - 1) - 2 \\ an = - 7 + 24 \times ( - 2) \\ an = - 7 + ( - 48) \\ an = - 7 - 48 \\ an = - 55 \\ \\ \\ \geqslant \: a \: soma \: dos \: termos \: da \: pa \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{( - 7 + ( - 55) \: )25}{2} \\ \\ sn = \frac{( - 7 - 55)25}{2} \\ \\ sn = \frac{ - 62 \times 25}{2} \\ \\ sn = - 31 \times 25 \\ \\ sn = - 775 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \leqslant \geqslant \geqslant$

Answer 2

Explicação passo-a-passo:

PA (-7,-9,-11,...)

Encontrar a razão da PA:

r = a₂ - a₁

r = -9 - (-7)

r = -2

Encontrar o valor do termo a₂₅:

aₙ = a₁ + (n - 1) . r

a₂₅ = -7 + (25 - 1) . (-2)

a₂₅ = -7 + (24) . (-2)

a₂₅ = -7 - 48

a₂₅ = -55

Somar dos 25 primeiros termos da PA:

$\rm S_n=\dfrac{(a_1+a_n)\cdot n}{2}$

$\rm S_{25}=\dfrac{( -7-55)\cdot25}{2}$

$\rm S_{25}=\dfrac{(-62)\cdot 25}{2}$

S₂₅ = -31 . 25

$\boxed{\boxed{\rm S_{25}=-775}}$