Question

Qual a soma dos termos desse PA (20;25;30.....980)

Answer 1

a₁ = 20
a₂ = 25
a₃ = 30
r = 25 - 20 = 5
an = 980
        an = a₁ + (n - 1) * r
        980 = 20 + (n - 1) * 5
        980 = 20 + 5n - 5
        980 - 20 = 5n - 5
        960 = 5n - 5
        5n = 960 + 5
        5n = 965
        n = 965 / 5
        n = 193

Soma dos termos da PA:
S = (a₁ + an) * n / 2
S = (20 + 980) * 193 / 2
S = 1000 * 193 / 2
S = 193000 / 2
S = 96500

Espero ter ajudado. Valeu!

Answer 2

Temos que descobrir quantos termos tem essa PA:

$PA (20;25;30.....980)\\\\ a_1=20\\ a_n=980\\ r=5\\n=?\\\\\\ a_n=a_1+(n-1)*r\\\\\\980=20+(n-1)*5\to \\\\ 980=20+5n-5\to \\\\ 980-20+5=5n\to\\\\ 965=5n\to\\\\ \frac{965}{5} =n\to\\\\ n=193$

Agora passamos à soma dos termos:

$S_n= \frac{(a_1+a_n)*n}{2} \\\\\\ S_n= \frac{(20+980)*193}{2} \\\\S_n= \frac{(1000)*193}{2} \\\\S_n= \frac{193000}{2} \\\\S_n=96500$