Find the 6th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7.

Here's how the sequence should go (first 4 terms):

1.....2.....3.....4
7, 7/3, 7/9, 7/27

Notice how I started with 7 and multiplied it by the common ratio (1/3) to determine the second term. Multiplying the latter by 1/3 again gives you the next term, and so on.

Use the pattern to find the sixth term.

Why did the geometric sequence go to the doctor? Because it had common "ratio" problems!

Anyway, let's calculate the 6th term of the sequence. The formula for the nth term of a geometric sequence is given by:

aₙ = a₁ * r^(n-1)

Here, a₁ is the first term (7) and r is the common ratio (1/3).

So, to find the 6th term (a₆), we have:

a₆ = 7 * (1/3)^(6-1)
= 7 * (1/3)^5
= 7 * (1/243)
= 7/243

So, the 6th term of the sequence is 7/243. Keep on calculating!

To find the 6th term of a geometric sequence, you need to know the common ratio and the first term. In this case, the common ratio is 1/3 and the first term is 7.

The formula to find the nth term of a geometric sequence is:
a_n = a_1 * r^(n-1)

where:
a_n is the n-th term of the sequence
a_1 is the first term of the sequence
r is the common ratio
n is the term number you want to find

Now, let's plug in the given values into the formula to find the 6th term:
a_6 = 7 * (1/3)^(6-1)

First, simplify the exponent:
a_6 = 7 * (1/3)^5

Next, calculate the value of (1/3)^5:
a_6 = 7 * (1/243)

Finally, multiply 7 by (1/243) to find the 6th term:
a_6 ≈ 0.0288

Therefore, the 6th term of the geometric sequence is approximately 0.0288.

A table of values of a linear function is shown below. Find the output when the input is n.

Input 1 2 3 4 n

Output 2 1 0 -1 ?

7/243