Given a geometric sequence with a1 = 6 and r = 2/3, write an explicit formula for An, the nth term of the sequence.
a r(n-1)
An = 6 (2/3)^(n-1)
If a1=-6 and r=−
1
3what will be the second term of the sequence?
The explicit formula for the nth term (An) of a geometric sequence is given by:
An = a1 * r^(n-1)
Given that a1 = 6 and r = 2/3, we can substitute the values into the formula to find the explicit formula for An:
An = 6 * (2/3)^(n-1)
Therefore, the explicit formula for the nth term of the given geometric sequence is An = 6 * (2/3)^(n-1).
To write an explicit formula for the nth term of a geometric sequence, we can use the formula:
An = a1 * r^(n-1)
Where:
- An represents the nth term of the sequence
- a1 is the first term of the sequence
- r is the common ratio of the sequence
- n represents the position of the term we want to find
In this case, you have been given a1 = 6 and r = 2/3. Plugging these values into the formula, we get:
An = 6 * (2/3)^(n-1)
Thus, the explicit formula for the nth term of the given geometric sequence is An = 6 * (2/3)^(n-1).