Question

Quanto vale a soma dos 50 primeiros termos da p.a. (-3,2,7...)?

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: aritmetica \\ \\ r = a2 - a1 \\ r = 2 - ( - 3) \\ r = 2 + 3 \\ r = 5 \\ \\ = = = = = = = = = = = = = = = = \\ \\ > \: o \: 50 \: termo \: da \: pa \\ \\ a50 = a1 + 49r \\ a50 = - 3 + 49 \times 5 \\ a50 = - 3 + 245 \\ a50 = 242 \\ \\ \\ = = = = = = = = = = = = = = \\ \\ \\ > \: a \: soma \: dos \: termos \: da \: pa \\ \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{( - 3 + 242)50}{2} \\ \\ sn = \frac{239 \times 50}{2} \\ \\ sn = 239 \times 25 \\ \\ sn = 5975 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant \geqslant$

Answer 2

Resposta: S₅₀ = 5975.

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Cálculo do termo a₅₀:

$\mathsf{ a_n=a_1+(n-1)\cdot r}$

$\mathsf{a_{50}=-3+ (50-1)\cdot5 }$

$\mathsf{ a_{50}=-3+49\cdot5}$

$\mathsf{a_{50}=-3+245 }$

$\mathsf{ a_{50}= 242}$

A somar dos 50 primeiros termos:

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

$\mathsf{S_{50}=\dfrac{(-3+242)\cdot50}{2} }$

$\mathsf{S_{50}=\dfrac{239\cdot50}{2} }$

$\mathsf{S_{50}=239\cdot25 }$

$\boxed{\boxed{ \mathsf{ S_{50}= 5975}}}$