Given:
[tex]2\frac{1}{4},2\frac{3}{4},3\frac{1}{4},3\frac{3}{4},.......[/tex]Required:
To find the next term in the given sequence.
Explanation:
Clearly the given sequence is in arithmetic.
Therefore,
[tex]a_5=a+(n-1)d[/tex]Here,
[tex]\begin{gathered} a=2\frac{1}{4} \\ =\frac{9}{4} \\ \\ n=5 \\ \\ d=2\frac{3}{4}-2\frac{1}{4} \\ =\frac{11}{4}-\frac{9}{4} \\ =\frac{2}{4} \end{gathered}[/tex][tex]\begin{gathered} a_5=\frac{9}{4}+(5-1)\frac{2}{4} \\ \\ =\frac{9}{4}+2 \\ \\ =\frac{17}{4} \\ \\ =4\frac{1}{4} \end{gathered}[/tex]Final Answer:
The next term in the sequence is 4 1/4.
