Determine the common ratio r, the fifth term, and the nth term of the geometric sequence.7, 145, 2825, 56125, . . .r = a5 = an =
Question
Determine the common ratio r, the fifth term, and the nth term of the geometric sequence.7, 145, 2825, 56125, . . .r = a5 = an =
Solution
The common ratio (r) of a geometric sequence can be found by dividing any term by the previous term.
Let's find r:
r = 145 / 7 = 20.714285714285715
Now, let's find the fifth term (a5). In a geometric sequence, any term is the product of the previous term and the common ratio.
a5 = 56125 * r = 56125 * 20.714285714285715 = 1161328.5714285714
The nth term (an) of a geometric sequence can be found using the formula:
an = a * r^(n-1)
where a is the first term and n is the term number.
So,
an = 7 * (20.714285714285715)^(n-1)
So, the common ratio r is approximately 20.714, the fifth term a5 is approximately 1161328.57, and the nth term an is 7 * (20.714285714285715)^(n-1).
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