Respuesta :
[tex]14\frac{1}{2},\text{ 12}\frac{3}{4},\text{ 11, }9\frac{1}{4},\text{ }7\frac{1}{2},\text{5}\frac{3}{4},\text{ }4,\text{ 2}\frac{1}{4},\text{ }\frac{1}{2}[/tex]
1) Examining this Sequence, we have an Arithmetic Sequence whose ratio is
r = -7/4, therefore we can fill in the gaps by adding each term to -7/4, so we have:
[tex]\begin{gathered} 14\frac{1}{2},\text{ 12}\frac{3}{4},\text{ 11, }9\frac{1}{4},\text{ }7\frac{1}{2},\text{5}\frac{3}{4},\text{ }4,\text{ 2}\frac{1}{4},\text{ }\frac{1}{2} \\ 11\text{ -}\frac{7}{4}\text{ =}\frac{37}{4}\text{ or 9}\frac{1}{4} \\ \frac{37}{4}-\frac{7}{4}=\frac{15}{2}\text{ or } \\ \frac{15}{2}-\frac{7}{4}=\frac{23}{4}\text{ or 5}\frac{3}{4} \\ \frac{23}{4}-\frac{7}{4}=\frac{16}{4}\text{ = 4} \\ 4-\frac{7}{4}=\frac{9}{4} \end{gathered}[/tex]Since in an Arithmetic Sequence each term is obtained by adding or subtracting a common ratio, in this case, r= -7/4
2) To transform a mixed number into a fraction, we need to keep the denominator from the original mixed number, and write the numerator as the product of the denominator by the whole number and add to the numerator:
[tex]\text{9}\frac{1}{4}=\frac{(4\text{ }\times9+1)}{4}=\frac{37}{4}[/tex]To turn an improper fraction into a mixed number we need to divide the numerator by the denominator and write the whole number and the fraction
[tex]\begin{gathered} \frac{37}{4}=9.25\text{ = 9 + }\frac{1}{4}\text{ =9}\frac{1}{4} \\ \frac{1}{4}\text{ =0.25} \end{gathered}[/tex]