Let's solve this step by step.

1. Let the first term in the sequence be $a$.
2. According to the problem, to get from one term to the next, we multiply by 2 and then add 4.

So, we have the following relationships:

• Second term: $a \cdot 2 + 4$
• Third term: $(a \cdot 2 + 4) \cdot 2 + 4$

We are given that the third term is 44.

Step-by-Step Calculation

1. Starting with the second term: $\text{Second term} = a \cdot 2 + 4 = 2a + 4$

2. Then, the third term (starting from the second term) would be: $\text{Third term} = (2a + 4) \cdot 2 + 4$ Simplify this expression: $= 4a + 8 + 4$ $= 4a + 12$

3. We know that the third term is 44, so we can set up the equation: $4a + 12 = 44$

4. Solving for $a$: $4a = 44 - 12$ $4a = 32$ $a = 8$

Answer

The first term in the sequence is 8.

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What would be the second term in this sequence if the first term is 8?
2. How would the sequence change if, instead of adding 4, we subtracted 4 after each multiplication?
3. Can you find a general formula for the $n$-th term in this sequence?
4. What would the fifth term in the sequence be with the first term as 8?
5. How does the sequence behave if we multiply by a different number each time?

Tip: For sequences with repeated operations (like multiplication and addition), forming equations step-by-step helps solve for unknown terms effectively.