نویسنده : امیر انصاری

1. $$
   6 + 9 + 12 + \text{…} (S_{10})
   $$
   
2. $$
   4.5+8+11.5+\text{...} (S_{12})
   $$
   
3. $$
   6+3+0+\text{...} (S_{10})
   $$
   
4. $$
   60+70+80+\text{...}(S_{20})
   $$
   

پاسخ

1. $$
   d= 9-6=3\\
   S_n=\frac{n}{2} \biggl[ 2t_1 + (n-1)d \biggr]\\
   S_{10}=\frac{10}{2} \biggl[ 2(6)+(10-1)(3) \biggr]\\
   S_{10}= 5 (12+27)\\
   S_{10}=195
   $$
   
2. $$
   d=8-4.5=3.5\\
   S_n=\frac{n}{2} \biggl[ 2t_1 + (n-1)d \biggr]\\
   S_{12}=\frac{12}{2} \biggl[ 2(4.5)+(12-1)(3.5) \biggr] \\
   S_{12}= 285
   $$
   
3. $$
   d=3-6=-3\\
   S_n=\frac{n}{2} \biggl[ 2t_1 + (n-1)d \biggr]\\
   S_{10}=\frac{10}{2} \biggl[ 2(6)+(10-1)(-3) \biggr]\\
   S_{10}=-75
   $$
   
4. $$
   d=70-60=10\\
   S_n=\frac{n}{2} \biggl[ 2t_1 + (n-1)d \biggr]\\
   S_{20}=\frac{20}{2} \biggl[ 2(60)+(20-1)(10) \biggr]\\
   S_{20}=3100
   $$