Answer:
![12(3 + 4 + 5 + ...... + 12 + 13) = 1056](https://img.qammunity.org/2021/formulas/mathematics/middle-school/fubj37zf4rv6mg7mpki5nagvwbxlv3psmo.png)
Explanation:
Given:
The attached
Required
Find the value of the expression
The interpretation of is to add the sequence: 12n
where n = from 3 to 13
Solving the for each term of the sequence
![When\ n = 3, 12n = 12(3)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/9qj4zr4g10gr1herqv94nr5nfo55x0fj1x.png)
![When\ n = 4, 12n = 12(4)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/rh3ihtfmm29n3eg8gk0mjnla9bw40tnog7.png)
![When\ n = 5, 12n = 12(5)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/6n28y4h1aw0qs7j6nvx97lsvb6b4u4stoe.png)
....................
...........
...
.
![When\ n = 12, 12n = 12(12)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/woqkasmpe7mfaan4a36qeat3q53pp2fcky.png)
![When\ n = 13, 12n = 12(13)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/2yjwldp0g149l82emwtk10dphojao8rcg7.png)
The sum is then calculated as follows;
![Sum = 12(3) + 12(4) + 12(4) + ...... + 12(12) + 12(13)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/p7kw0njjw70dw518szhvyvxmcz83ntm7dy.png)
12 is a common factor;
Hence;
![Sum = 12(3 + 4 + 5 + ...... + 12 + 13)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/s5x6v708t2urux8apv2rxopc69nyhx8vjl.png)
Replace ....... with actual numbers
![Sum = 12(3 + 4 + 5 +6 + 7 + 8 + 9 + 10 + 11 + 12 + 13)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/er3ka9zv0iw92m6x1lshqj70k25dxzznai.png)
![Sum = 12(88)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/hvo5tvu76cag0j2vg88md2gyxjds0exo7r.png)
![Sum = 1056](https://img.qammunity.org/2021/formulas/mathematics/middle-school/onw9l9rk2pex94kkei0nt8dde5hoinyf8e.png)
Hence;
![12(3 + 4 + 5 + ...... + 12 + 13) = 1056](https://img.qammunity.org/2021/formulas/mathematics/middle-school/fubj37zf4rv6mg7mpki5nagvwbxlv3psmo.png)
From the list of given options;
Option B is correct
![12(3 + 4 + 5 + ...... + 12 + 13) = 1056](https://img.qammunity.org/2021/formulas/mathematics/middle-school/fubj37zf4rv6mg7mpki5nagvwbxlv3psmo.png)