Question

What is the next term of the following sequence?

20, 10, 5, 2 1/2, ...

1 1/2
1 1/4
3/4

Answer 1

I believe the answer is 1 1/4 because if you look at the pattern, as you go farther to the right the numbers are divided by 2(half), so 2 1/2 ÷ 2 =1 1/4
In order to divide a mixed number and a whole number you must covert the mixed number into a improper fraction.

Answer 2

Answer: The correct option is (B)
`1(1)/(4).`

Step-by-step explanation: We are given to find the next term in the folloing sequence:

`20,~~10,~~5,~~2(1)/(2),~~.~~.~~.\\\\=20,~~10,~~5,~~(5)/(2),~~.~~.~~.`

We see that the consecutive terms of the above sequence is related by the relation:

`(10)/(20)=(5)/(10)=((5)/(2))/(5)=~~.~~.~~.=(1)/(2).`

So, if
`a_n` denotes the n-th term of the sequence, then

`(a_2)/(a_1)=(a_3)/(a_2)=(a_4)/(a_3)=~~.~~.~~.=(1)/(2)\\\\\Rightarrow a_2=(1)/(2)a_1,~~a_3=(1)/(2)a_2,~~a_4=(1)/(2)a_3,~.~.~.`

Hence, the given sequence is a geometric sequence with first term 20 and common ratio
`(1)/(2).`

So, the next (fifth) term of the sequence will be

`a_5=(1)/(2)a_4=(1)/(2)* (5)/(2)=(5)/(4)=1(1)/(4).`

Thus, the next term of the given sequence is
`1(1)/(4).`

Option (B) is correct.