What the general term a_n for the geometric sequence
a_1= -5 and a_2= 15
To find the general term of a geometric sequence, we need to find the common ratio (r) first.
The common ratio (r) is found by dividing any term by the term that precedes it.
In this case, we will divide the second term (a₂) by the first term (a₁):
r = a₂/a₁ = 15/(-5) = -3
Now that we have the common ratio (r), we can find the general term (aₙ) of the geometric sequence.
The general term (aₙ) is given by the formula:
aₙ = a₁ * r^(n-1)
Substituting the values we know:
a₁ = -5
r = -3
We can now substitute these values into the formula to find the general term (aₙ):
aₙ = -5 * (-3)^(n-1)
Therefore, the general term (aₙ) for the given geometric sequence is -5 * (-3)^(n-1).