Write an equation for the nth term of the geometric sequence 11, -33, 99, -297
well, it's clear that r = -3, so ...
Sure, here's the equation:
nth term = 11 * (-3)^(n-1)
To find the equation for the nth term of a geometric sequence, we need to identify the common ratio (r) and the first term (a₁).
Given the sequence: 11, -33, 99, -297
The common ratio is found by dividing any term by the previous term.
The common ratio (r) = -33 / 11 = -3 = 99 / -33 = -3 = -297 / 99 = -3
So, the common ratio (r) of the geometric sequence is -3.
Now we need to find the first term (a₁). The first term (a₁) is simply the value of the first term in the sequence, which is 11 in this case.
Now that we have the value of the common ratio (r) and the first term (a₁), the equation for the nth term of this geometric sequence can be written as:
aₙ = a₁ * r^(n - 1)
Substituting the values:
aₙ = 11 * (-3)^(n - 1)
Thus, the equation for the nth term of the geometric sequence 11, -33, 99, -297 is aₙ = 11 * (-3)^(n - 1).
To find the equation for the nth term of a geometric sequence, we need to identify the common ratio (r) between consecutive terms.
In this sequence, we can observe that each term is obtained by multiplying the preceding term by -3. Thus, the common ratio (r) is -3.
The first term (a₁) in the sequence is 11.
Now, we can use the formula for the nth term of a geometric sequence:
nth term (Tn) = a₁ * r^(n-1)
Plugging in the values we have:
Tn = 11 * (-3)^(n-1)
Therefore, the equation for the nth term of the geometric sequence 11, -33, 99, -297 is:
Tn = 11 * (-3)^(n-1)