Question

1. a₁=2, r=6

Explanation:

Assuming we need to find the terms of a geometric sequence or its sum, let's recall the formula for the \(n\)-th term of a geometric sequence: \(a_n = a_1 \cdot r^{n - 1}\), and the sum of the first \(n\) terms \(S_n=\frac{a_1(1 - r^n)}{1 - r}\) (for \(r
eq1\)).

Step 1: Identify the type of problem (assuming finding the first few terms)

We have the first term \(a_1 = 2\) and common ratio \(r = 6\) for a geometric sequence.

Step 2: Find the second term (\(a_2\))

Using the formula \(a_n=a_1\cdot r^{n - 1}\), for \(n = 2\):
\(a_2=a_1\cdot r^{2 - 1}=a_1\cdot r\)
Substitute \(a_1 = 2\) and \(r = 6\):
\(a_2=2\times6 = 12\)

Step 3: Find the third term (\(a_3\))

For \(n = 3\):
\(a_3=a_1\cdot r^{3 - 1}=a_1\cdot r^{2}\)
Substitute \(a_1 = 2\) and \(r = 6\):
\(a_3=2\times6^{2}=2\times36 = 72\)

(If we need the sum, for example, sum of first 3 terms:
\(S_3=\frac{2(1 - 6^{3})}{1 - 6}=\frac{2(1 - 216)}{-5}=\frac{2(-215)}{-5}=\frac{-430}{-5}=86\))

Answer:

If finding the second term: \(12\); third term: \(72\); sum of first 3 terms: \(86\) (depending on the exact requirement, but based on the given \(a_1 = 2\), \(r = 6\) for a geometric sequence, these are common calculations).