Question

a soma dos termos da PA (2,6,10,...82)

Answer 1

PA (2,6,10,...82) 
a₁ = 2
r = a₃ - a₂
r = 10 - 6 
r = 4
an = a₁ + (n-1)r
an = 2 + ( n - 1 ) 4
82 = 2 + (n -1)4
n -1 = (82 - 2) ÷ 4
n = 11

an = 82

            ( a₁ + an )n                      ( 2 + 82 )11       924
Sn = -----------------        ⇒ S₁₁ = -------------     = ---------- = 462
                  2                                      2                     2

S₁₁ = 462

bons estudos um abraço.

Answer 2

$a _{n} = a_{1} +r(n-1) \\ \\ r=6-2=4 \\ \\ 82=2+4(n-1) \\ \\ 82-2=4(n-1) \\ \\ 80=4(n-1) \\ n-1= \frac{80}{4} \\ \\ n=20+1 \\ \\ n=21 \\ \\ S _{n} = \frac{( a_{1}+ a_{n})n }{2} \\ \\ S_{21} = \frac{(2+82)21}{2} \\ \\ S_{21} =42.21 \\ \\ S_{21} =882$