Math Problem Statement
berilah jawaban serta rumusnya
Solution
The problem discusses Mr. Anton, a duck farmer who collects eggs, with the number of eggs forming an arithmetic sequence. We are given the following information:
- Mr. Anton collects a total of 9,000 eggs over 3 months (90 days, since ).
- On the first day, he collects 30 eggs.
- We are asked to find how many eggs he collects on the last day.
Step-by-Step Solution:
-
Identify the Arithmetic Sequence:
- The total number of days is (since 3 months = 90 days).
- The first term of the sequence is (he collects 30 eggs on the first day).
- Let the number of eggs collected on the last day (day 90) be , which is the value we need to find.
-
Sum of the Arithmetic Sequence: The sum of an arithmetic sequence is given by the formula: Where:
- (the total number of eggs),
- ,
- ,
- is the number of eggs on the last day.
Substituting the values we know: Simplifying: Solving for :
Thus, the number of eggs collected on the last day is 170 eggs.
Final Answer:
Mr. Anton collects 170 eggs on the last day.
Would you like further explanation or details on any part of the solution?
Here are 5 related questions to expand on this concept:
- How would the answer change if Mr. Anton collected 40 eggs on the first day instead of 30?
- How would you determine the common difference in this arithmetic sequence?
- Can you calculate the total number of eggs collected after the first 45 days?
- What would be the sum if the total period was 120 days instead of 90 days?
- How do arithmetic sequences relate to geometric sequences in terms of growth patterns?
Tip: Always remember that the sum of an arithmetic sequence is directly influenced by the number of terms and the average of the first and last terms.
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequence
Sum of Arithmetic Series
Formulas
S = n/2 * (a + l)
l = (S - a * n/2) / n
Theorems
Arithmetic Series Sum Formula
Suitable Grade Level
Grades 9-11
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