For the geometric sequence, -100,50,-25,12.5, find the next two terms and the general term.
the common ratio can be found by dividing any term by the previous one.
clearly r = -1/2
So, Tn = -100 (-1/2)^(n-1) = 200/(-2)^n
To find the next two terms and the general term of the geometric sequence, we need to determine the common ratio (r) first.
The common ratio (r) is found by dividing any term of the sequence by the previous term. Let's calculate it:
r = 50 / (-100) = -0.5
Now that we know the common ratio, we can find the next two terms. The nth term of a geometric sequence can be found using the formula:
an = a1 * r^(n-1)
where:
an = nth term
a1 = first term
r = common ratio
n = term number
Let's calculate the next two terms:
a5 = (-100) * (-0.5)^(5-1) = (-100) * (-0.5)^4 = (-100) * 0.0625 = -6.25
a6 = (-100) * (-0.5)^(6-1) = (-100) * (-0.5)^5 = (-100) * 0.03125 = -3.125
Therefore, the next two terms are -6.25 and -3.125.
Now let's find the general term of the sequence:
an = a1 * r^(n-1)
Substituting the first term (-100) and the common ratio (-0.5) into the formula, we have:
an = -100 * (-0.5)^(n-1)
So the general term of the sequence is -100 * (-0.5)^(n-1).