Question

2. Calcule a soma dos 25 primeiros termos de uma P.A. que tem a₁ = 3 er =4.​

Answer 1

$> \: resolucao \\ \\ \geqslant \: progressao \: \: aritmetica \\ \\ a1 = 3 \\ r = 4 \\ \\ = = = = = = = = = = = = = = = = \\ \\ \\ > \: o \: 25 \: termo \: da \: pa \\ \\ an = a1 + (n - 1)r \\ an = 3 + (25 - 1)4 \\ an = 3 + 24 \times 4 \\ an = 3 + 96 \\ an = 99 \\ \\ = = = = = = = = = = = = = = = = \\ \\ \\ > \: soma \: dos \: termos \: da \: pa \\ \\ \\ sn = \frac{(a1 + an)n}{2} \\ \\ sn = \frac{(3 + 99)25}{2} \\ \\ sn = \frac{102 \times 25}{2} \\ \\ sn = 51 \times 25 \\ \\ sn = 1275 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant$

Answer 2

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

$\mathsf{a_{25}=3+(25-1)\cdot4 }$

$\mathsf{ a_{25}=3+24\cdot4}$

$\mathsf{a_{25}=3+96 }$

$\mathsf{a_{25}=99 }$

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

$\mathsf{ S_{25}=\dfrac{(3+99)\cdot25}{2}}$

$\mathsf{ S_{25}=\dfrac{ 102\cdot25}{2}}$

$\mathsf{S_{25}=51\cdot25 }$

$\red{ \mathsf{S_{25}= 1275} }$