Question

Find the 8th term in the following sequence.

32, 16, 8, 4, ..

02
O 114
O 1/2
O 1

Answer 1

Answer is 1/4
Option ‘B’

Answer 2

The 8th term in the sequence is \( \frac{1}{2} \).

Step-by-step explanation:

The given sequence is a geometric progression where each term is obtained by multiplying the preceding term by a constant factor. In this case, to find the common ratio, we can divide any term by its preceding term. For example,
`\((16)/(32) = (1)/(2)\).` This indicates that the common ratio (r) is
`\( (1)/(2) \).`

Now, we can use the formula for the nth term of a geometric sequence,
`\(a_n = a_1 * r^((n-1))\), where \(a_n\) is the nth term, \(a_1\)` is the first term, (r) is the common ratio, and (n) is the term number. In our case,
`\(a_1 = 32\), \(r = (1)/(2)\), and \(n = 8\).` Plugging these values into the formula, we get:

`\[a_8 = 32 * \left((1)/(2)\right)^((8-1))\]`

`\[a_8 = 32 * \left((1)/(2)\right)^7\]`

`\[a_8 = (32)/(2^7) = (32)/(128) = (1)/(4)\]`

Therefore, the 8th term in the sequence is
`\( (1)/(4) \),` and the answer is
`\( (1)/(2) \).` This implies that the terms in the sequence are halved at each step, leading to the identified pattern and the solution.