Math Problem Statement
Solution
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 ). For each subsequent term, you increase the amount added by 1.
Here’s how you would proceed:
- First term:
- Second term:
- Third term:
- Fourth term:
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:
- How can you generalize the formula for the -th term in this sequence?
- How does this sequence relate to arithmetic sequences?
- Can you derive a formula to find the sum of the first terms?
- What happens if the regularly increasing amount grows larger than the first term?
- 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.
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Math Problem Analysis
Mathematical Concepts
Sequences
Recurrence Relations
Arithmetic Progression
Formulas
T_n = T_{n-1} + ( -4 + (n-1) )
Theorems
Arithmetic sequence formula
Suitable Grade Level
Grades 7-9
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