It is known that {an} satisfies an = (3N + 1) 2 ^ (n + 1), and Sn is obtained by subtraction of dislocation

It is known that {an} satisfies an = (3N + 1) 2 ^ (n + 1), and Sn is obtained by subtraction of dislocation

According to the theme
Sn=4×2^2+7×2^3+10×2^4+… +(3n+1)×2^(n+1)
Therefore, the equation is multiplied by the common ratio 2 of the equal ratio sequence to get:
2Sn=4×2^3+7×2^4+10×2^5+… +(3n+1)×2^(n+2)
So 2Sn Sn = Sn = - 4 × 2 ^ 2 - [3 × 2 ^ 3 + 3 × 2 ^ 4 + +3×2^(n+1)]+(3n+1)×2^(n+2)
=-16-3[2^3+2^4+2^5+… +2^(n+1)]+(3n+1)×2^(n+2)
=-16-3[-2^3+2^(n+2)]+(3n+1)×2^(n+2)
Well organized
=(3n-2)×2^(n+2)+8
Checked calculation