Given the explicit formula : a5=8+ (5-1) 3
what is the common inital term
The common initial term, also known as the first term, can be found by substituting 1 for n in the formula.
So, the common initial term (a1) is:
a1 = 8 + (1-1) * 3
= 8 + 0 * 3
= 8 + 0
= 8
Therefore, the common initial term is 8.
The common initial term refers to the value of the first term in the number sequence. In this case, the explicit formula given is a5 = 8 + (5-1) * 3.
To find the common initial term, you need to determine the value of a1.
By plugging the value of "5" into the formula, you can solve for a5:
a5 = 8 + (5-1) * 3
= 8 + 4 * 3
= 8 + 12
= 20
Since a5 represents the fifth term in the sequence, you can calculate a1 by subtracting 4 from a5:
a1 = a5 - (5-1) * 3
= 20 - 4 * 3
= 20 - 12
= 8
Therefore, the common initial term (a1) in this sequence is 8.
To find the common initial term in the explicit formula, we need to identify the pattern or rule being used.
In the given formula, the pattern is the multiplication of the term number by a constant value and adding a constant term. The general form of an explicit formula for a sequence is:
an = a1 + (n-1)d
Where:
an is the nth term in the sequence
a1 is the first term in the sequence
n is the position of the term being calculated
d is the common difference between consecutive terms
In the given formula, a5 = 8 + (5-1)*3. Here, a5 represents the fifth term in the sequence. By comparing this with the general form, we can deduce that the constant term, a1, is 8. Therefore, the common initial term in the given explicit formula is 8.