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anonymous

  • one year ago

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.

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  1. anonymous
    • one year ago
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    i got 1205 for the total but the answer choices want another number.

  2. mathstudent55
    • one year ago
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    The first year is the first term of a sequence. \(a_1 = 350\) \(a_2 = 350 + 1 \times 45\) \(a_3 = 350 + 2 \times 45\) \(a_n = a_1 + (n - 1)45\)

  3. mathstudent55
    • one year ago
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    This is an arithmetic sequence with the common difference being 45.

  4. anonymous
    • one year ago
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    a.$1205;$15,550 b.$1250;$16,000 c.$1250;$32,000 d.$1205;$31,100

  5. mathstudent55
    • one year ago
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    \(\large a_{n} = a_1 + (n - 1)45\) \(\large a_{20} = 350 + (20 - 1)45\) \(a_{20} = 1205\)

  6. mathstudent55
    • one year ago
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    $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.

  7. anonymous
    • one year ago
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    ok so like 395 for the second year

  8. anonymous
    • one year ago
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    440 for the 3rd year?

  9. mathstudent55
    • one year ago
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    Yes. There is a formula we can use for the sum.

  10. mathstudent55
    • one year ago
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    \(\Large S_n = \dfrac{n(a_1 + a_n)}{2} \)

  11. mathstudent55
    • one year ago
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    The sum of terms 1 to term n is the formula above.

  12. anonymous
    • one year ago
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    ok

  13. mathstudent55
    • one year ago
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    \(\Large S_{20} = \dfrac{20(350 + 1205)}{2} \)

  14. anonymous
    • one year ago
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    n=45?

  15. anonymous
    • one year ago
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    ok 20=n ai=350 an=1205...i see.

  16. mathstudent55
    • one year ago
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    No. n is the number of terms we are adding. Here it is 20.

  17. anonymous
    • one year ago
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    got it, i have a test over this tomorrow, im nervous. how can you tell this word problem apart from others?

  18. mathstudent55
    • one year ago
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    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.

  19. anonymous
    • one year ago
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    ok i understand now. i really appreciate your help! @mathstudent55

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