I cannot figure this out!
What is the series (the Pattern) of this sequence?
{1,5,1,5,1,5,1,5.......}
That is a sequence, not a series.
A sequence is an ordered list of terms.
A series is a sum of terms, which may be terms in a sequence.
so
1,5,1,5,1,5..... is a sequence
but
1+5+1+5+1+5..... would be a series
the pattern of your sequence could be said to be alternating 1 and 5
To determine the series or pattern of the given sequence {1, 5, 1, 5, 1, 5, 1, 5, ...}, let's analyze the numbers and their positions:
Position 1: 1
Position 2: 5
Position 3: 1
Position 4: 5
Position 5: 1
Position 6: 5
By observing the sequence, we can see that the pattern alternates between the numbers 1 and 5. In other words, the sequence repeats itself with every two numbers.
To mathematically represent this pattern, we can say that the nth term of the sequence is equal to (n % 2) + 1, where % denotes the modulo operation. This formula would return 1 for every odd position and 2 for every even position.
For example:
- Position 1: 1 % 2 + 1 = 1 + 1 = 2
- Position 2: 2 % 2 + 1 = 0 + 1 = 1
- Position 3: 3 % 2 + 1 = 1 + 1 = 2
- Position 4: 4 % 2 + 1 = 0 + 1 = 1
Therefore, the series or pattern of the given sequence is that the value alternates between 1 and 2 for every two positions.