To get from one term to the next in a sequence, we multiply by 2 and then add 4 . The third term in the sequence is 40 . What is the first term in the sequence?

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Denote first term as a: Let's denote the first term of the sequence as a. According to the rule of the sequence, to get the second term, we multiply the first term by 2 and then add 4. So, the second term can be represented as 2a + 4.Calculate second term: Similarly, to get the third term from the second term, we multiply the second term by 2 and then add 4. Therefore, the third term is 2(2a + 4) + 4. We know that the third term is given as 40. So we can set up the equation 2(2a + 4) + 4 = 40.Calculate third term: Now, let's solve the equation for a. First, we distribute the 2 inside the parentheses: 2 * 2a + 2 * 4 + 4 = 40, which simplifies to 4a + 8 + 4 = 40.Set up equation: Combine the constant terms on the left side: 4a + 12 = 40.Solve for a: Subtract 12 from both sides to isolate the term with a: 4a + 12 - 12 = 40 - 12, which simplifies to 4a = 28.Find first term: Finally, divide both sides by 4 to solve for a: 4a / 4 = 28 / 4, which gives us a = 7. This is the first term of the sequence.

To get from one term to the next in a sequence, we multiply by $2$ and then add $4$ . $\newline$ The third term in the sequence is $40$ . $\newline$ What is the first term in the sequence?

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To get from one term to the next in a sequence, we multiply by $2$ and then add $4$ . $\newline$ The third term in the sequence is $40$ . $\newline$ What is the first term in the sequence?