## 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.

1. anonymous

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

2. mathstudent55

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

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

4. anonymous

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

5. mathstudent55

$$\large a_{n} = a_1 + (n - 1)45$$ $$\large a_{20} = 350 + (20 - 1)45$$ $$a_{20} = 1205$$

6. mathstudent55

$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 ok so like 395 for the second year 8. anonymous 440 for the 3rd year? 9. mathstudent55 Yes. There is a formula we can use for the sum. 10. mathstudent55 $$\Large S_n = \dfrac{n(a_1 + a_n)}{2}$$ 11. mathstudent55 The sum of terms 1 to term n is the formula above. 12. anonymous ok 13. mathstudent55 $$\Large S_{20} = \dfrac{20(350 + 1205)}{2}$$ 14. anonymous n=45? 15. anonymous ok 20=n ai=350 an=1205...i see. 16. mathstudent55 No. n is the number of terms we are adding. Here it is 20. 17. anonymous got it, i have a test over this tomorrow, im nervous. how can you tell this word problem apart from others? 18. mathstudent55 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

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