IDNLearn.com makes it easy to find answers and share knowledge with others. Get the information you need from our experts, who provide reliable and detailed answers to all your questions.

Evaluate the summation of 3 n plus 2, from n equals 1 to 14. 39 49 340 343.

Sagot :

The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

How to find the sum of consecutive integers?

[tex]1 + 2 + 3 + ... + n = \dfrac{n(n+1)}{2}[/tex]


What are the properties of summation?

[tex]\sum_{i=r}^s (a \times f(i) + b) = a \times [\: \sum_{i=r}^s f(i)] + (s-r)b[/tex]

where a, b, r, and s are constants, f(i) is function of i, i ranging from r to s (integral assuming).

For the given case, the considered summation can be written symbolically as:

[tex]\sum_{n=1}^{14} (3n + 2)[/tex]

It is evaluated as;

[tex]\sum_{n=1}^{14} (3n + 2) = 3 \times [ \: \sum_{n=1}^{14} n ] + \sum_{n=1}^{14} 2\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times \dfrac{(14)(14 + 1)}{2} + (2 + 2 + .. + 2(\text{14 times}))\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times 105 + 28 = 343\\[/tex]

Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343

Learn more about summation here:

https://brainly.com/question/14322177