Question

Evaluate 14
∑ 3n + 2
n=1

Answer 1

`\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`

Answer 2

343

Explanation:

The given expression is

`\sum_(n=1)^(14)(3n+2)`

We need to find the value of this expression.

`\sum_(n=1)^(14)3n+\sum_(n=1)^(14)2`

`3\sum_(n=1)^(14)n+2\sum_(n=1)^(14)1`

We know that ,

`1+2+3+...+n=(n(n+1))/(2)`

`3(1+2+3+...+14)+2(1+1+1+...+1(14 times))`

`3* (14(14+1))/(2)+2(14)`

`3* 105+28`

`315+28`

`343`

Therefore, the value of given expression is 343.