Respuesta :
[tex]\bf \displaystyle\sum_{n=1}^{14}~3n+2\implies \sum_{n=1}^{14}~3n+\sum_{n=1}^{14}~2\implies 3\sum_{n=1}^{14}~n+\sum_{n=1}^{14}~2 \\\\\\ 3\left[ \cfrac{14(14+1)}{2} \right]+[(14)(2)]\implies 3[7(15)]+[28]\implies 3(105)+[28] \\\\\\ 315+28\implies 343[/tex]
Answer:
343
Step-by-step explanation:
The given expression is
[tex]\sum_{n=1}^{14}(3n+2)[/tex]
We need to find the value of this expression.
[tex]\sum_{n=1}^{14}3n+\sum_{n=1}^{14}2[/tex]
[tex]3\sum_{n=1}^{14}n+2\sum_{n=1}^{14}1[/tex]
We know that ,
[tex]1+2+3+...+n=\dfrac{n(n+1)}{2}[/tex]
[tex]3(1+2+3+...+14)+2(1+1+1+...+1(14 times))[/tex]
[tex]3\times \dfrac{14(14+1)}{2}+2(14)[/tex]
[tex]3\times 105+28[/tex]
[tex]315+28[/tex]
[tex]343[/tex]
Therefore, the value of given expression is 343.
