Sequences

Describe the pattern in the sequence. Find the next three terms   1, 2, 6, 16, 44,...

• A.  Add the two previous terms and then multiply by 2; 120, 328, 896
• B. Multiply by 2 and then add 4; 92, 188, 380
• C. Alternate multiplying by 2 and by 3; 88, 264, 528
• D. Add all the previous terms; 69, 138, 276

Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.

• A.  9.2 feet
• B.  10.8 feet
• C.   7.8 feet
• D.  1.9 feet

Write a recursive formula for the sequence
15, 26, 48, 92, 180, .... Then find the next term.

• A.  a_n = 2a_n-1  -  4, a₁ = 15;  356
• B.  a_n = 2a_n  -  4, a₁ = 15;  356
• C.  a_n = 4 + 11⋅ 2^n-1, a₁ = 15;  356
• D.  a_n = 3a_n-1  -  19, a₁ = 15;  356

Write an explicit formula for the sequence
7, 2, –3, –8, –13, ...
Then find a₁₄.

• A.  a_n = -5n  +  12;  -53
• B.  a_n = -5n  +  7;  -58
• C.  a_n = -5n  +  12;  -58
• D.  a_n = -5n  +  7;  -63

The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria.

• A.  a_n = 19n  +  19
• B.  a_n = n  +  19
• C.  a_n = (1/19)n  
• D.  a_n = 19n  

Is the formula
 a_n = -4n(n - 1) 
is explicit or recursive? Find the first five terms of the sequence.

• A.  recursive; 1, –4, 16, –64, 256 
• B.  recursive; 0, –16, –24, –48, –80
• C.  explicit; 1, –4, 16, –64, 256
• D.  explicit; 0, –8, –24, –48, –80

Find the 50th term of the sequence
5, –2, –9, –16, ...

• A.  -352
• B.  -343
• C.  -338
• D.  -331

Find the missing term of the arithmetic sequence 22,  ₹  , 34,...

• A.  46
• B.  16
• C.  28
• D.  40

Write the explicit formula for the sequence. Then find the fifth term in the sequence.  
a₁ = 3, r = -3

• A.  a_n = 3 ⋅ (-3)^{n - 1} ; 243
• B.  a_n = -3 ⋅ (3)^{n - 1} ; -243
• C.  a_n = 3 ⋅ (3)ⁿ  ; 243
• D.  a_n = 3 ⋅ (-3)ⁿ ; -729