Number of terms in this sequence 1/128, 1/64,1/32,.........,32,64 is
To find the number of terms in a sequence, we need to determine the pattern and the last term.
The pattern in this sequence is that each term is double the previous term.
Starting with 1/128 and doubling it, we find the following terms:
1/128, 1/64, 1/32, 1/16, 1/8, 1/4, 1/2, 1, 2, 4, 8, 16, 32, 64
The last term is 64.
To find the number of terms in this sequence, we need to count how many terms there are from 1/128 to 64.
If we continue to double the terms from 1/128, we will eventually reach 64. We only need to count how many times we need to double 1/128 to get to 64.
In each doubling, we multiply by 2. So, if we divide 64 by 1/128, we can find out how many times we need to double 1/128 to get to 64:
64 / (1/128) = 64 * 128 = 8192
Therefore, there are 8192 terms in this sequence.
To find the number of terms in a sequence, we need to determine the pattern and the difference between each term.
In this sequence, the first term is 1/128, and the common ratio can be calculated by dividing any term by the previous term:
(1/64) / (1/128) = 128/64 = 2
Since each term is obtained by multiplying the previous term by 2, there is a common ratio of 2 in this sequence.
Now, we need to find the term where the sequence ends, which is 64. Let's express 64 as a fraction with the same denominator as the first term:
64 = (128/2) = (1/128) * 2^7
So, the seventh term in the sequence is 64. Therefore, the number of terms in the sequence is 7.
To find the number of terms in a sequence, we need to determine the pattern or rule that governs the sequence and use it to find the next term until we reach the desired term.
Looking at the given sequence, we can observe that each term is obtained by successively multiplying the previous term by 2.
Let's start with the first term, which is 1/128. We will multiply this term by 2 repeatedly until we reach the last term, which is 64.
1/128 * 2 = 1/64
1/64 * 2 = 1/32
1/32 * 2 = 1/16
1/16 * 2 = 1/8
1/8 * 2 = 1/4
1/4 * 2 = 1/2
1/2 * 2 = 1
As we can see, the sequence continues until we reach 1.
Now, let's count the number of terms in this sequence. Starting from the first term, we have:
1/128, 1/64, 1/32, 1/16, 1/8, 1/4, 1/2, 1
There are 8 terms in this sequence.
Therefore, the number of terms in the given sequence is 8.