Identify the Sequence 1 , 1/2 , 1/4 , 1/8 , 1/16 , 1/32 (2024)

FAQs

Identify the Sequence 1 , 1/2 , 1/4 , 1/8 , 1/16 , 1/32? ›

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 12 gives the next term.

It is a geometric sequence.

The series of numbers 1, 2, 4, 8, 16 ... is an example of a geometric sequence, sometimes called a geometric progression (GP).

Explanation: The sequence you provided: 1/2, 1/4, 1/8,... is a geometric sequence. A geometric sequence is a sequence where each next term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. In your sequence, each term is half or 0.5 times the previous term.

The sequence appears to be dividing the previous term by 2. 1/8, 1/16, 1/32 are the next 3 terms in the sequence.

Summary: The general term for the sequence 2, 4, 8, 16, 32, . . . is a_n = 2ⁿ.

The sequence 1,2,4,8,16,… is a geometric sequence with common ratio 2, since each term is obtained from the preceding one by doubling. The sequence 9,3,1,1/3,… is a geometric sequence with common ratio 1/3.

2, 4, 8, 16, 32, 64, 128, 256,… In this sequence has a factor of 2 between each number. Each term is found by multiplying the previous term by 2. Hence, 32*2=64 and so on .

Geometric Sequence

1, 2, 4, 8, 16, 32, 64, 128, ...

The common ratio of GP 4,8,16,32,..... is. 2.

What is the sum to infinity of 1, 2, 1, 4, 1, 8, 1, 16? ›

Answer: The sum of infinite GP series 1/2 , 1/4 , 1/8 , 1/16 ... is 1.

Explanation: The sequence {1,12,14,18,..} is a geometric series of the type {a,a,ar2,ar3,....} , in which a - the first term is 1 and ratio r between a term and its preceding term is 12 .

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 12 gives the next term. In other words, an=a1rn−1 a n = a 1 r n - 1 . This is the form of a geometric sequence.

Detailed Solution

Given Series: 2, 1, (1/2), (1/4) ... Hence, the correct answer is "(1/8)".

The number that comes next in the sequence 1/2, 4, 1/8, 16, is 2. This sequence is based on a pattern of alternating multiplication by 4 and division by 8.

These are the first number on each row of Floyd's triangle. As the third column of Bernoulli's triangle (k = 2) is a triangular number plus one, it forms the lazy caterer's sequence for n cuts, where n ≥ 2. 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, ...

Answer. This is an arithmetic sequence since there is a common difference between each term. In this case, adding 3 to the previous term in the sequence gives the next term.

The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ... Each number, starting with the third, adheres to the prescribed formula.

Answer: The sum of infinite GP series 1/2 , 1/4 , 1/8 , 1/16 ... is 1.