Question

Describe a pattern in the sequence of numbers. Predict the next number.

1.) 256, 64, 16, 4, ... ________.
2.) 2, 6, 18, 54, ... _______

Answer 1

`{ \qquad\qquad\huge\underline{{\sf Answer}}}`

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

`\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = (1)/(4)`

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

• That is : 1/4 × 4 = 1

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

`\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3`

So, the next term is 3 times the preceding term, that is :

• 3 × 54 = 162

Therefore, the next term is 162

Answer 2

1.
pattern: divide by 4
next term: 1

2.
pattern: multiply by 3
next term: 162