Answer:
1) The first term is $138
2) The difference is $55
3) The iterative rule for the amount of money Mrs. Speas has after n weeks is 27.5·n² + 110.5·n
Step-by-step explanation:
The mount Mrs. Speas has in her bank account = $138
The amount of money she deposits each week = $55
The amount of money in Mrs. Speas account therefore, forms an Arithmetic Progression
1) The first term = a = The initial money Mrs. Speas has in her bank account = $138
2) The (common) difference = d =The amount she deposits at the end of each week = $55
The iterative rule for the amount of money Mrs. Speas has (in her bank account) after n weeks is given by the formula for the sum of an arthmetic progression (AP), Sₙ, as follows;
[tex]S_n = \dfrac{n}{2} \times \left [2 \times a + (n - 1)\times d \right ][/tex]
Substituting the values of a and d gives;
[tex]S_n = \dfrac{n}{2} \times \left [2 \times 138 + (n - 1)\times 55 \right ] = \dfrac{n}{2} \times \left [221 + n \times 55 \right ] = 110.5\cdot n + 27.5 \cdot n^2[/tex]
∴ 3) The amount of money she has after n weeks = Sₙ = 27.5·n² + 110.5·n.
