Respuesta :

d = 3 , a₁₂ = 40 and S[tex]x_{100}[/tex] = 7775

In an arithmetic sequence the nth term and sum to n terms are

• a[tex]n[/tex] = a₁ + (n-1)d

• S[tex]_n[/tex] = [tex]\frac{n}{2}[/tex][2a + (n-1)d]

where d is the common difference

a₆ = a₁ + 5d = 22 ⇒ 7 + 5d = 22 ⇒ 5d = 15 ⇔ d = 3

a₁₂ = 7 + 11d = 7 +( 11× 3) = 7 + 33 = 40

S₁₀₀ = [tex]\frac{50}{2}[/tex][(2×7) +(99×3)

      = 25(14 + 297) = 25(311)= 7775

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