Find the indicated term of the geometric sequence.
a1 = 7, a4 = 189/8 , 8th term
term 4 = ar^3 = 189/8
but a = 7
7r^3 = 189/8
r^3 = 189/56
r^3 = 27/8
r = 3/2
so term(8) = .... , use your formula for term 8
8
16
Using the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where a1 is the first term and r is the common ratio between each term.
We know a1 = 7, and we found the common ratio to be r = 3/2.
So, to find the 8th term:
a8 = 7 * (3/2)^(8-1)
a8 = 7 * (3/2)^7
a8 = 7 * 2187/128
a8 = 11907/128
a8 ā 93.05
Therefore, the 8th term of the sequence is approximately 93.05.
Why did the geometric sequence go to the circus? To find the 8th term, of course!
We can use the formula for the nth term of a geometric sequence to solve this: an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the position of the term we're looking for.
In this case, a1 = 7, a4 = 189/8, and we want to find the 8th term. Let's plug these values in and solve for r:
a4 = a1 * r^(4-1)
189/8 = 7 * r^3
To make the math easier, let's rewrite 189/8 as a decimal: 23.625.
23.625 = 7 * r^3
Divide both sides by 7:
3.375 = r^3
Now, to find the 8th term, we can use the formula again:
a8 = a1 * r^(8-1)
a8 = 7 * r^7
Plug in the value of r we found:
a8 = 7 * (3.375)^7
And that's your answer! I hope the geometric sequence enjoyed its time at the circus.
To find the 8th term of a geometric sequence, we need to know the common ratio (r) of the sequence.
The common ratio (r) is found by dividing any term in the sequence by the previous term. In this case, we can use a4 and a3 to find the common ratio.
a4 = 189/8
a3 = a4/r
To find r, we can rearrange the equation and solve for r:
r = a4 / a3
r = (189/8) / a3
Now, let's find a3 using the information given in the problem.
a3 = a4 / r
a3 = (189/8) / ((189/8) / a3)
To simplify the equation, we can multiply both sides by a3 and divide both sides by (189/8):
a3^2 = a3 * (189/8) / (189/8)
a3^2 = a3
Since a3 is not equal to zero (0), we can divide both sides by a3:
a3 = 1
Now that we know a3, we can find the common ratio (r):
r = (189/8) / a3
r = (189/8) / 1
r = 189/8
Now, we can use the formula to find the nth term of a geometric sequence:
an = a1 * r^(n-1)
We want to find the 8th term (a8), so n = 8:
a8 = a1 * r^(8-1)
a8 = 7 * (189/8)^(7)
a8 ā 83465.625
Therefore, the 8th term of the geometric sequence is approximately 83465.625.