Find the First Five Terms of the Sequence

Pre-CalculusName______

Assignment: K10

Find the first five terms of the sequence.

1. 2.

3. 4.

Find the sum.

5.6.

7. Write the sum without sigma notation.

Write the sum using sigma notation.

8. 2 + 4 + 6 + + 209.

Determine whether the sequence is arithmetic or geometric, then find the nth term of the sequence.

10. 3, 6, 9, 12, …11. 27, -9, 3, -1, …

12. The 12th term of an arithmetic sequence is 32 and the fifth term is 18. Find the 20th term.

13. Which term of the arithmetic sequence 1, 5, 9, … is 401?

14. The common ratio in a geometric sequence is , and the fifth term is 1. Find the 2nd term.

15. Find the partial sum of the arithmetic sequence with the given conditions: a = 3, d = 2, n = 12.

16. Find the sum of the arithmetic sequence: 0.7 + 2.7 + 4.7 + + 56.7

17. Find the sum of the arithmetic sequence:

18. The first term of an arithmetic sequence is 1 and the fourth term is 16. How many terms of this sequence must be added to get 2356?

19. Find the partial sum of the geometric sequence with the given conditions: a = , r = , n = 4.

20. Find the sum of the geometric sequence:

21. Find the sum of the geometric sequence:

22. Find the sum of the infinite geometric series:

23. Express as a fraction. YOU MUST SHOW WORK FOR THIS!!!!

24. Find the amount of an annuity that consists of 24 monthly payments of $500 each into an account that pays 8% interest per year, compounded monthly.

25. How much money should be invested every quarter at 10% per year, compounded quarterly, in order tohave $5000 in 2 years?

26. A couple can afford to make a monthly mortgage payment of $650. If the mortgage rate is 9% and the couple intends to secure a 30-year mortgage, how much can they borrow?

27. What is the monthly payment on a 30-year mortgage of $80,000 at 9% interest?

a) What is the monthly payment on this same mortgage if it is to be repaid over a 15-year period?

b) What is the total amount paid on this loan over a 15-year period?

28. Jane agrees to buy a car for a down payment of $2000 and payments of $220 per month for 3 years. If the interest rate is 8% per year, compounded monthly, what is the actual purchase price of her car?

Expand the expression (you can use EITHER Pascal’s Triangle or the Binomial Theorem).

29.

30.

31.

32.

33.Find the 20th term of the expansion.

34.Find the 26th term of the expansion.

35.Find the first three terms in the expansion of.

36.Find the last three terms in the expansion of.

37.Find the term containing in the expansion of.

38.Find the term containing in the expansion of.

Answers:

1. 1, 6, 15, 28, 45 2. -8, -4, -2, -1, -1/2 3. 3, -1, 3, -1, 3 4. 1, 4, 27, 256, 3125 5. 306. 12

7. -1 + 1 + 3 + 5 + ...+ 97 + 99 8. 9. 10. Arithmetic, an = 3n

11. Geometric, 12. a20 = 48 13. n = 101st term 14. 15. S12 = 168

16. S29 = 832.3 17. S21 = -399 18. n = 31 terms 19. 20. 21.

22. 2 23. 24. Af = $12,971.67 25. R = $572.34 26. AP = $80,783.21 27. R = $643.70;

27a) R = $811.41; 27b) $146,053.80 28. $7,016.46 29.

30. 31.

32. 33. 34. 35.

36. 37. 38.