Question

What is the next term of the following sequence?

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) $1\dfrac{1}{4}.$

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

$20,~~10,~~5,~~2\dfrac{1}{2},~~.~~.~~.\\\\=20,~~10,~~5,~~\dfrac{5}{2},~~.~~.~~.$

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

$\dfrac{10}{20}=\dfrac{5}{10}=\dfrac{\dfrac{5}{2}}{5}=~~.~~.~~.=\dfrac{1}{2}.$

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

$\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=~~.~~.~~.=\dfrac{1}{2}\\\\\Rightarrow a_2=\dfrac{1}{2}a_1,~~a_3=\dfrac{1}{2}a_2,~~a_4=\dfrac{1}{2}a_3,~.~.~.$

Hence, the given sequence is a geometric sequence with first term 20 and common ratio $\dfrac{1}{2}.$

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

$a_5=\dfrac{1}{2}a_4=\dfrac{1}{2}\times \dfrac{5}{2}=\dfrac{5}{4}=1\dfrac{1}{4}.$

Thus, the next term of the given sequence is $1\dfrac{1}{4}.$

Option (B) is correct.