A sequence is defined as follows :
`a_(a)=4, a_(n)=2a_(n-1)+1, ngt2`, find `(a_(n+1))/(a_(n))` for n=1, 2, 3.

Answer

To solve the problem step by step, we will first determine the terms of the sequence defined by the recurrence relation and then calculate the ratios as required.

### Step 1: Find the first term \( a_1 \)
Given:
\[ a_1 = 4 \]

### Step 2: Find the second term \( a_2 \)
Using the formula:
\[ a_n = 2a_{n-1} + 1 \]
For \( n = 2 \):
\[ a_2 = 2a_1 + 1 = 2 \times 4 + 1 = 8 + 1 = 9 \]

### Step 3: Find the third term \( a_3 \)
Using the same formula for \( n = 3 \):
\[ a_3 = 2a_2 + 1 = 2 \times 9 + 1 = 18 + 1 = 19 \]

### Step 4: Find the fourth term \( a_4 \)
Using the formula for \( n = 4 \):
\[ a_4 = 2a_3 + 1 = 2 \times 19 + 1 = 38 + 1 = 39 \]

### Step 5: Calculate \( \frac{a_{n+1}}{a_n} \) for \( n = 1, 2, 3 \)

1. For \( n = 1 \):
\[ \frac{a_{2}}{a_{1}} = \frac{9}{4} \]

2. For \( n = 2 \):
\[ \frac{a_{3}}{a_{2}} = \frac{19}{9} \]

3. For \( n = 3 \):
\[ \frac{a_{4}}{a_{3}} = \frac{39}{19} \]

### Final Results:
- For \( n = 1 \): \( \frac{a_{2}}{a_{1}} = \frac{9}{4} \)
- For \( n = 2 \): \( \frac{a_{3}}{a_{2}} = \frac{19}{9} \)
- For \( n = 3 \): \( \frac{a_{4}}{a_{3}} = \frac{39}{19} \)