The first term of a geometric sequence is -400, and the common ratio is
4/5
.
What is the 8th term of the sequence?
To find the 8th term of the geometric sequence, we can use the formula:
nth term = first term * (common ratio)^(n-1)
In this case, the first term is -400 and the common ratio is 4/5.
So the 8th term would be:
8th term = -400 * (4/5)^(8-1)
Simplifying this expression:
8th term = -400 * (4/5)^7
Calculating (4/5)^7:
(4/5)^7 = (4^7) / (5^7) = 16384 / 78125 = 0.2097152
Multiplying by -400:
8th term = -400 * 0.2097152 = -83.88608
Therefore, the 8th term of the sequence is approximately -83.88608.
To find the 8th term of this geometric sequence, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
Where:
an is the nth term of the sequence,
a1 is the first term of the sequence,
r is the common ratio,
and n is the position of the term we want to find.
Given that the first term (a1) is -400 and the common ratio (r) is 4/5, we can substitute these values into the formula:
a8 = (-400) * (4/5)^(8-1)
Now let's calculate the value:
a8 = (-400) * (4/5)^7
= (-400) * (16384/78125)
= -65536/78125
Therefore, the 8th term of the sequence is -65536/78125.
To find the 8th term of a geometric sequence, you can use the formula:
term(n) = a * r^(n-1)
Where:
- term(n) is the nth term of the sequence
- a is the first term of the sequence
- r is the common ratio
- n is the position of the term you want to find
In this case, the first term (a) is -400, the common ratio (r) is 4/5, and we want to find the 8th term (n = 8).
Plugging these values into the formula:
term(8) = -400 * (4/5)^(8-1)
Simplifying the exponent:
term(8) = -400 * (4/5)^7
Evaluating the power:
term(8) = -400 * (16384/78125)
Simplifying the fraction:
term(8) = -400 * 16384 / 78125
Calculating the product:
term(8) = -819200 / 78125
Dividing the numerator by the denominator:
term(8) ≈ -10.5
Therefore, the 8th term of the sequence is approximately -10.5.