Arithmetic Progressions

The following are Arithmetic Progressions, except

• 12, 6, 3, ...

• 4, 2, 0, ...

• x, x+2, x+4, ...

• $\frac{1}{2},\ 0,\ -\frac{1}{2},\ ...$

To determine whether a sequence of numbers is an Arithmetic Progression, you can conduct a test on

• $T_1-T_2=T_3-T_2$

• $T_2-T_1=T_2-T_3$

• $T_2-T_1=T_3-T_1$

• $T_2-T_1=T_4-T_3$

Given the AP 4, p, q, r, ... with a common difference of -2, determine the value of r.

• r = 0

• r = 1

• r = -2

• r = -4

Given the AP 18, x, ... , -12, -14, determine the value of x.

• x = 17

• x = 16

• x = 14

• x = 12

What is the formula for finding the value of the  $n^{th}$  term of an AP?

•  $T_n=a-\left(n+1\right)d$  

•  $T_n=d+\left(n-1\right)a$  
  

•  $T_n=a+\left(n+1\right)d$  

•  $T_n=a+\left(n-1\right)d$  

What is the formula for the  $n^{th}$  term of the AP   $\frac{2}{3},\ 1,\ \frac{4}{3},\ ...$  

•  $T_n=\frac{1}{3}\left(n-1\right)$  

•  $T_n=\frac{1}{3}\left(n+1\right)$  

•  $T_n=\frac{2}{3}\left(n+1\right)$  

•  $T_n=\frac{2}{3}\left(n-1\right)$  

Given the AP 5, 8, 11, ... , which term has the value of 272?

• 88

• 89

• 90

• 91

The $n^{th}$  term of an AP is given by   $T_n=\ 2\ -3n$  , find the common difference.

• -3

• -4

• -5

• -6

The $10^{th}$ term  of the AP  y, y + 2, y + 4 , ... is 16, find the value of y.

• -4

• -2

• 0

• 2

The 7^th term of an AP is 3 times the 2^nd term, find a relation between a and d.

• $a=\frac{3}{2}d$

• $a=\frac{2}{3}d$

• $a=\frac{1}{2}d$

• $a=3d$