Given the explicit formula : a5=8+ (5-1) 3
what is the common differance
The common difference is the difference between any two consecutive terms in an arithmetic sequence.
In this case, we can see that the fifth term is obtained by adding 8 to 3 times the difference between 5 and 1. So the difference between the fifth term and the fourth term is 3.
Therefore, the common difference is 3.
To find the common difference in a sequence, we need to examine the difference between consecutive terms.
In the given formula: a5 = 8 + (5-1) * 3, we can see that it represents the 5th term of the sequence.
The formula suggests that the term is obtained by starting with 8 and adding the product of (5-1) multiplied by 3.
To find the common difference, we need to find the difference between consecutive terms. In this case, we need to find the difference between the 5th term and the 4th term.
To find the 4th term, we can substitute n=4 into the formula:
a4 = 8 + (4-1) * 3 = 8 + 3 * 3 = 8 + 9 = 17
Now, we can find the difference between the 5th term (a5) and the 4th term (a4):
a5 - a4 = (8 + (5-1) * 3) - (8 + (4-1) * 3)
= (8 + 4 * 3) - (8 + 3 * 3)
= (8 + 12) - (8 + 9)
= 20 - 17
= 3
Therefore, the common difference in this sequence is 3.
In the given explicit formula a₅ = 8 + (5 - 1)3, the common difference can be determined by comparing consecutive terms in the arithmetic sequence.
The general formula for an arithmetic sequence is aₙ = a₁ + (n - 1)d, where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.
In this case, we can identify that the first term a₁ = 8. The position of the term n = 5. Substituting these values into the formula, we have:
a₅ = 8 + (5 - 1)d
Simplifying further:
a₅ = 8 + (4)d
Now, comparing this with the given formula a₅ = 8 + (5 - 1)3, we can equate the expressions:
8 + (4)d = 8 + (5 - 1)3
We see that both equations are the same. Thus, the common difference d in the given formula is equal to 3.