Algebra - Chapter 12 (Sequences and Series)

Find the first, second, and sixth terms of

 $a_n=\frac{3}{\left(n^2+1\right)}$  .

•  $\frac{3}{2};\ \frac{3}{5};\ \frac{3}{13}$  
  

•  $\frac{3}{2};\ \frac{3}{5};\ \frac{3}{37}$  
  

•  $\frac{3}{2};\ \frac{3}{5};\ \frac{3}{7}$  
  

•  $\frac{3}{2};\ \frac{3}{5};\ \frac{3}{10}$  

State the next term for the sequence.

5.3, 5.7, 6.1, 6.5, 

•  $\frac{6}{9}$ 

• 69

• 0.69

• 6.9

Which of the following sequences is arithmetic?

• 1, 1, 2, 3, 5, ...

• 0, 1, 3, 6, 10, ...

• -11.77, -15.07, -18.37, -21.67, -24.97, ...

•  $1,\ \frac{1}{4},\ \frac{1}{7},\ \frac{1}{10},\ \frac{1}{13},\ ...$  
  

Write both a recursive formula and a simplified explicit formula for the sequence

5, 11, 17, 23, 29, ....

• a_n = a_n-1 + 6

  
  

  a_n = 6n - 1

• a_n = a_n-1 + 6, where a₁ = 5

  
  

  a_n = 5n

• a_n = a_n-1 + 6

  
  

  a_n = 5n

• a_n = a_n-1 + 6, where a₁ = 5

  
  

  a_n = 6n - 1

Find the two arithmetic means between -17 and 16.

• -17, -6, 5, 16, 27, ...

• 27, 38

• -6, 5

• -17, -6

Write an explicit formula for

 $-\frac{2}{3},\ \frac{4}{7},\ -\frac{8}{11},\ \frac{16}{15},\ ...$  .

•  $a_n=\frac{\left(-2\right)^n}{4n-1}$  

•  $a_n=-\frac{2n}{4n-1}$  

•  $a_n=-\frac{2^n}{4n-1}$  

•  $a_n=\frac{2^n}{4n-1}$  

Which of the following sequences is geometric?

• 32, -16, 4, -2, ...

• 0.25, 0.5, 1, 2, ...

• 5, 11, 17, 23, ...

• 1, 8, 27, 64, ...

Write both a recursive formula and a simplified explicit formula for the sequence

2, 10, 50, 250, 1 250, ....

• a_n = 0.4a_n-1

  
  

  a_n = 6n - 1

• a_n = 5a_n-1, where a₁ = 2

  
  

  a_n = 0.4(5ⁿ)

• a_n = 5a_n-1, where a₁ = 2

  
  

  a_n = 0.4(5ⁿ) + 8

• a_n = 5a_n-1

  
  

  a_n = 0.4(5ⁿ)

Find the three geometric means between 2 and 162.

• -6, 18, -54,

• 6, 18, -54

• 6, 18, 45

• 6, 81, 54

Find the indicated term of the arithmetic sequence.

a₂₂ if a₇ = 22 and a₁₅ = -10

• -20

• 20

• 38

• -38