Question

1. a₁ = -4, r = 4

Explanation:

Assuming we need to find the first few terms of a geometric sequence with first term \(a_1 = - 4\) and common ratio \(r = 4\).

Step 1: Recall the formula for geometric sequence terms

The \(n\)-th term of a geometric sequence is given by \(a_n=a_1\times r^{n - 1}\)

Step 2: Find the first term (\(n = 1\))

We know \(a_1=-4\) (given)

Step 3: Find the second term (\(n = 2\))

Using the formula \(a_2=a_1\times r\)
Substitute \(a_1=-4\) and \(r = 4\)
\(a_2=-4\times4=-16\)

Step 4: Find the third term (\(n = 3\))

Using the formula \(a_3=a_2\times r\) (or \(a_3=a_1\times r^{2}\))
Substitute \(a_2=-16\) and \(r = 4\)
\(a_3=-16\times4=-64\)

Step 5: Find the fourth term (\(n = 4\))

Using the formula \(a_4=a_3\times r\) (or \(a_4=a_1\times r^{3}\))
Substitute \(a_3=-64\) and \(r = 4\)
\(a_4=-64\times4=-256\)

Answer:

If we are finding the first few terms of the geometric sequence, the first four terms are \(-4,-16,-64,-256\) (depending on what is required, if it's to find terms, this is the result. If it's another operation related to geometric sequence with these values, the approach would be similar using the geometric sequence formula)