Math Problem Statement
Solution
Let's solve the problem step by step.
Part (a): Writing a formula for the sequence
Charlie initially deposits $115 into the account. Each week thereafter, he deposits $35. This forms an arithmetic sequence where:
- The first term is .
- The common difference is .
The general formula for an arithmetic sequence is:
Where:
- is the amount deposited after weeks,
- is the initial amount ($115),
- is the amount added each week ($35).
So, the formula becomes:
Part (b): Total money deposited after 30 weeks
To find the total deposited after 30 weeks, we need to sum the sequence up to .
The sum of the first terms of an arithmetic sequence is:
Plugging in the values:
So, the total money deposited after 30 weeks is $18,675.
Would you like further details or have any questions?
Related Questions:
- What is the total amount deposited after 10 weeks?
- What if the initial deposit was $200 instead of $115? How would the formula change?
- How much would be deposited after 52 weeks (1 year)?
- How would the sum formula look if the deposit amount per week increased by $5 each month?
- Can you write the recursive formula for this sequence?
Tip:
Always identify whether a problem involves arithmetic or geometric sequences by examining whether the change between terms is constant (arithmetic) or multiplicative (geometric).
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Math Problem Analysis
Mathematical Concepts
Arithmetic Sequences
Algebra
Formulas
General formula for an arithmetic sequence: a_n = a + (n - 1) · d
Sum of first n terms of an arithmetic sequence: S_n = (n/2) · (2a + (n - 1) · d)
Theorems
Arithmetic Sequence Formula
Sum of Arithmetic Sequence Formula
Suitable Grade Level
Grades 7-9
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