https://file.aiquickdraw.com/mathbot/file/1727409096046hnqfww7x.jpg

The problem shown in the image asks you to calculate a sequence where each term is the previous term plus an increasing amount.

The first term is 74. To get the second term, you are instructed to subtract 4 (add \(-4\)). For each subsequent term, you increase the amount added by 1.

Here’s how you would proceed:

1. First term: \( 74 \)
2. Second term: \( 74 + (-4) = 70 \)
3. Third term: \( 70 + (-3) = 67 \)
4. Fourth term: \( 67 + (-2) = 65 \)

Each time, you reduce the negative number being added by 1 (so the value added increases by 1 in absolute terms).

Would you like me to continue the sequence or provide further details?

Here are 5 related questions you might explore:
1. How can you generalize the formula for the \(n\)-th term in this sequence?
2. How does this sequence relate to arithmetic sequences?
3. Can you derive a formula to find the sum of the first \(n\) terms?
4. What happens if the regularly increasing amount grows larger than the first term?
5. How would this sequence change if the starting number was different?

**Tip**: Sequences like this can often be described using a recurrence relation, which is a way of defining a sequence based on its previous terms.

The problem asks for the next terms in a sequence where the first term is 74, the second term is obtained by adding -4, and each subsequent term is calculated by increasing the amount added by 1.

Explore how to solve a sequence problem where each term is calculated by adding a regularly increasing amount. The first term is 74, and the amount added to each subsequent term starts at -4, increasing by 1. Suitable for Grades 7-9.

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