Answer:
[tex]\displaystyle S_{27}=675[/tex]
Step-by-step explanation:
The sum of N consecutive natural numbers is given by:
[tex]\displaystyle S_N=\frac{N}{2}(F+L)[/tex]
We need to find the sum of the natural numbers between 12 to 38.
To calculate the required sum we have F=12, L=38, but we don't have the value of N.
From 12 to 38 there are 38 - 12 + 1 = 27 natural consecutive numbers, thus N=27.
Substituting in the formula:
[tex]\displaystyle S_{27}=\frac{27}{2}(12+38)[/tex]
[tex]\displaystyle S_{27}=\frac{27}{2}(50)[/tex]
[tex]\displaystyle S_{27}=27*25[/tex]
[tex]\mathbf{\displaystyle S_{27}=675}[/tex]
