Find the 8th term of the geometric sequence 7, -21, 63, ...7,−21,63
Looks like another of those posts where numerical stuff is duplicated. Haven't figured out why that happens so much.
If the sequence is 7, -21, 63 ...
then
a = 7
r = -3
and the 8th term is 7*(-3)^7 = -15309
With the gap "..." we don't know what the 8th term would be.
Thank you
To find the 8th term of the geometric sequence 7, -21, 63, ..., we need to determine the common ratio and then use the formula for the nth term of a geometric sequence.
A geometric sequence is a sequence where each term after the first is found by multiplying the preceding term by a fixed, non-zero number called the common ratio (r).
In this case, we can find the common ratio (r) by dividing any term by its preceding term. Let's choose the second and first terms, -21 and 7.
r = (-21) / 7
r = -3
So the common ratio (r) is -3.
Now, we can use the formula for the nth term of a geometric sequence:
nth term = a1 * r^(n-1)
In this formula, a1 represents the first term of the sequence, r is the common ratio, and n is the position of the term we want to find.
To find the 8th term, we substitute the values into the formula:
8th term = 7 * (-3)^(8-1)
8th term = 7 * (-3)^7
8th term ≈ 7 * (-2187)
8th term ≈ -15309
Therefore, the 8th term of the sequence 7, -21, 63, ... is approximately -15309.