Question

As part of her retirement savings plan, Patricia deposited $350.00 in bank account during her first year in the workforce. During each subsequent year, she deposited $45.00 more than the previous year. Find how much she deposited during her twentieth year in the workforce. Find the total amount deposited in the twenty years.

Answer 1

i got 1205 for the total but the answer choices want another number.

Answer 2

The first year is the first term of a sequence.
\(a_1 = 350\)
\(a_2 = 350 + 1 \times 45\)
\(a_3 = 350 + 2 \times 45\)

\(a_n = a_1 + (n - 1)45\)

Answer 3

This is an arithmetic sequence with the common difference being 45.

Answer 4

a.$1205;$15,550
b.$1250;$16,000
c.$1250;$32,000
d.$1205;$31,100

Answer 5

\(\large a_{n} = a_1 + (n - 1)45\)

\(\large a_{20} = 350 + (20 - 1)45\)

\(a_{20} = 1205\)

Answer 6

$1205 is the amount deposited just in the 20th year.

Now we need the sum of all deposits from the 1st year to the 20th year.

Answer 7

ok so like 395 for the second year

Answer 8

440 for the 3rd year?

Answer 9

Yes.
There is a formula we can use for the sum.

Answer 10

\(\Large S_n = \dfrac{n(a_1 + a_n)}{2} \)

Answer 11

The sum of terms 1 to term n is the formula above.

Answer 12

ok

Answer 13

\(\Large S_{20} = \dfrac{20(350 + 1205)}{2} \)

Answer 14

n=45?

Answer 15

ok 20=n ai=350 an=1205...i see.

Answer 16

No. n is the number of terms we are adding. Here it is 20.

Answer 17

got it, i have a test over this tomorrow, im nervous. how can you tell this word problem apart from others?

Answer 18

In this problem, we start with $350.
Then each year we add $45.
Since the amount for each subsequent year is 45 more, that means we have a constant difference.
This means we are dealing with an arithmetic sequence.

Answer 19

ok i understand now. i really appreciate your help! @mathstudent55