Question

What is the 6th term of the geometric sequence 2/25 , 2/5, 2 , 10 ?

Answer 1

The 6th term of the geometric sequence 2/25, 2/5, 2, 10 is 1250. This is found by using the common ratio 5 and multiplying the first term by 5 raised to the power of (n-1), where n is the term number.

Step-by-step explanation:

You've asked what the 6th term of the geometric sequence 2/25, 2/5, 2, 10 would be. To find this, we can determine the common ratio and then apply it to find subsequent terms. A geometric sequence is expressed as an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and an is the nth term.

First, we find the common ratio by dividing the second term by the first term: r = (2/5) ÷ (2/25) = 5. We can do a quick check by dividing the third term by the second term, and we find it's the same ratio (2 ÷ (2/5) = 5).

Using this ratio, we can find the 6th term: a6 = (2/25) × (5(6-1)) = (2/25) × (55) = 2 × (54).

Calculating 54, we get 625, so the 6th term is 2 × 625 = 1250.

Answer 2

to find the common ratio, divide the second term by the first term.
(2/5) / (2/25) = 2/5 * 25/2 = 50/10 = 5

an = a1 * r^(n-1)
n = term u want to find = 6
a1 = first term = 2/25
r = common ratio = 5

a6 = 2/25 * 5^(6-1)
q6 = 2/25 * 5^5
a6 = 2/25 * 3125
a6 = 6250/25
a6 = 250 <===