Câu 2:
a: Sai
b: \(u_8=u_1+7d=\frac32+\frac72=\frac{10}{2}=5\)
=>Đúng
c: Đặt \(\frac{15}{4}=u_1+n\cdot d\)
=>\(\frac12n+\frac32=\frac{15}{4}\)
=>\(\frac{n}{2}=\frac{15}{4}-\frac32=\frac{15}{4}-\frac64=\frac94\)
=>n=9/2(loại)
=>Sai
d: \(S_{100}=\frac{100\cdot\left\lbrack2\cdot u_1+99\cdot d\right\rbrack}{2}=50\cdot\left(2\cdot u_1+99\cdot d\right)\)
\(=50\left(2\cdot\frac32+99\cdot\frac12\right)=50\cdot\left(3+49,5\right)=50\cdot52,5=2625\)
=>Sai
Câu 3:
a: \(u_6=u_1+5d\)
=>\(5d=u_6-u_1=27-\left(-3\right)=30\)
=>d=6
=>sai
b: \(u_{85}=u_1+84d=-3+84\cdot6=501\)
=>Đúng
c: \(u_{10}=u_1+9d=-3+9\cdot6=-3+54=51\)
=>Sai
d: \(S_{85}=\frac{85\cdot\left\lbrack2\cdot u_1+84\cdot d\right\rbrack}{2}=85\cdot\left\lbrack u_1+42\cdot d\right\rbrack=85\cdot\left\lbrack-3+42\cdot6\right\rbrack=85\cdot249=21165\)
=>Đúng
Câu 4:
a: \(S_{50}=5150\)
=>\(50\cdot\frac{\left\lbrack2\cdot u_1+49\cdot d\right\rbrack}{2}=5150\)
=>\(25\cdot\left(2\cdot u_1+49\cdot d\right)=5150\)
=>\(2u_1+49d=\frac{5150}{25}=206\)
=>10+49d=206
=>49d=196
=>d=4
=>Sai
b: \(u_{85}=u_1+84d=5+84\cdot4=5+336=341\)
=>Đúng
c: \(u_{10}=u_1+9d=5+9\cdot4=5+36=41\)
=>Sai
d: \(S_{85}=85\cdot\frac{\left\lbrack2\cdot u_1+84d\right\rbrack}{2}=85\cdot\left(u_1+42d\right)\)
\(=85\cdot\left(5+42\cdot4\right)=85\cdot173=14705\)
=>Đúng
