Question

What is next in sequence 2 and 1/4, 2 and 3/4, 3 and 1/4 come in 3 and 3/4,

Answer 1

Given:

`2(1)/(4),2(3)/(4),3(1)/(4),3(3)/(4),.......`

Required:

To find the next term in the given sequence.

Step-by-step explanation:

Clearly the given sequence is in arithmetic.

Therefore,

`a_5=a+(n-1)d`

Here,

`\begin{gathered} a=2(1)/(4) \\ =(9)/(4) \\ \\ n=5 \\ \\ d=2(3)/(4)-2(1)/(4) \\ =(11)/(4)-(9)/(4) \\ =(2)/(4) \end{gathered}`
`\begin{gathered} a_5=(9)/(4)+(5-1)(2)/(4) \\ \\ =(9)/(4)+2 \\ \\ =(17)/(4) \\ \\ =4(1)/(4) \end{gathered}`

Final Answer:

The next term in the sequence is 4 1/4.