Question

Find the formula for the nth term of 1/64, 1/32, 1/16

Answer 1

Answer: The common ratio between each term is 2. We can write the first term as 1/64 = 2^-6. To find the other terms, we can multiply the first term by 2^n-1:

1st term: 2^-6

2nd term: 2^-5 = 2^-6 x 2^1

3rd term: 2^-4 = 2^-6 x 2^2

...

nth term: 2^(n-6) = 2^-6 x 2^n

Therefore, the formula for the nth term is:

an = 1/64 x 2^n-6

Answer 2

To find the formula for the nth term of the sequence 1/64, 1/32, 1/16, we can start by observing the pattern of the sequence.

The sequence is a geometric sequence, which means each term is obtained by multiplying the previous term by a constant ratio. In this case, the ratio between consecutive terms is 1/2.

To find the formula for the nth term, we can use the formula for the general term of a geometric sequence:

an = a1 * r^(n-1)

where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.

In this case, the first term a1 is 1/64 and the common ratio r is 1/2.

Therefore, the formula for the nth term of the sequence 1/64, 1/32, 1/16 is:

an = (1/64) * (1/2)^(n-1)

This formula allows you to find any term in the sequence by substituting the value of n into the formula. For example, to find the 4th term, you would substitute n = 4 into the formula:

a4 = (1/64) * (1/2)^(4-1)

= (1/64) * (1/2)^3

= (1/64) * (1/8)

= 1/512

Therefore, the 4th term of the sequence is 1/512.

Remember, when working with geometric sequences, it's important to pay attention to the given terms and identify the common ratio to find the formula for the nth term.

Explanation: