a Zachary started by depositing $50 into Angela's account when she turned 1 month old. After the initial deposit, he continues depositing $5 per month into Angela's account. We get the following arithmetic sequence.
Notice that since an arithmetic sequence increases linearly, we know that the amount he deposits on the month of Angela's second birthday is the same amount that he deposits on any other month, which is $5.
b Let's consider the general equation for an arithmetic sequence.
Arithmetic Sequence
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t(n)= m(n-1)+ t(1)
&Slope: m
&First term: t(1)
From Part A we know that the arithmetic sequence has a first term of 50 and a slope of 5. Let's substitute this into the formula.
c To determine the total amount of money on Angela's bank account on her first birthday, we can use the formula for calculating the sum of an arithmetic sequence.
S_n=n(a_1+a_n)/2To use this formula we need to know the last term of the sequence, a_n. Angela's first birthday is 12 deposits later. Therefore, we want to calculate t(12) using the formula from Part B.
