Practice with Arithmetic & Geometric sequence and series

Solve the following problems related to arithmetic and geometric sequences and series .

Look carefully at each question to determine the " who " your work order. 

You might want to have your graphing calculator handy.

1. Find the sum of the first term of the sequence 4, 6, 8, 10, .... Answer

2. Find the sum of the first term of the sequence -8, -5, -2, ..., 7  Answer

3. Find a₆ for an arithmetic sequence where a₁ = 3x+1 and d = 2x+6. Answer

4. How many terms of the arithmetic sequence -3, 2, 7, ... must be added together for the sum of the series to be 116?  Answer

5. Find the 9^th term of the sequence:  Answer

6. Evaluate this series using a formula:   Answer

7. Insert three geometric means between 1 and 81. Answer

8. Find t₁₂ for a geometric sequence where   t₁ = 2 + 2i   and   r = 3.  Answer

9. A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans.  How many cans, in total, are in the display?  Answer

10. Find the indicated sum:   Answer

11. Given the sequence -4, 0, 4, 8, 12, ..., Darius devises a formula for the sum of nterms of the sequence.  His formula is

Is this formula correct?  Show work to support your answer.

Answer

12. Which of the following choices is the formula for the nth term of the sequence 54, 18, 6, ... ?  

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You may try the question above to gain your knowledge..