Question

Allison decided to start by saving $10 the first week of the year in her bank. Then, the next week she would save $2 more dollars than the previous week and put that in the bank

Blank 1 Geometric or Arithmetic
Blank 2 Recursive Formula
Blank 3 Explicit Formula
Blank 4 If she kept increasing the amount in this way how much will she have to deposit on week 52 ?
a.$112
c.$3172
b.$114
d.$3340

Answer 1

Allison's saving plan follows an arithmetic sequence with an initial deposit of $10 and an increase of $2 each week. Using the explicit formula of an arithmetic sequence, we can determine that she will have to deposit $112 on week 52.

Step-by-step explanation:

Allison's saving plan follows an arithmetic sequence because the amount saved each week increases by a constant amount. This can be determined using the recursive formula:

an = an-1 + d

where an represents the amount saved in week n, an-1 represents the amount saved in week n-1, and d represents the constant difference between each consecutive term.

In this case, the first term a1 is $10 and the common difference d is $2.

Using the explicit formula for an arithmetic sequence:

an = a1 + (n-1)d

we can find the amount saved in week 52:

a52 = 10 + (52-1)2

Simplifying the equation:

a52 = 10 + 51*2

a52 = 10 + 102

a52 = 112

Therefore, Allison will have to deposit $112 on week 52.