IB AI - Sequences and Series Summative Quiz

State which sequence is arithmetic.

•  $a_n=1,\ 2,\ 3,\ 5,\ ...$  

•  $b_n=\ 1,\ \frac{3}{2},\ \frac{9}{4},\ \frac{27}{8},\ ...$  

•  $c_n=1,\ \frac{1}{2},\ \frac{1}{3},\ \frac{1}{4},\ ...$  

•  $d_n=\ 1,\ 0.95,\ 0.90,\ 0.85,\ ...$  

State which sequence is geometric.

•  $a_n=1,\ 2,\ 3,\ 5,\ ...$  

•  $b_n=\ 1,\ \frac{3}{2},\ \frac{9}{4},\ \frac{27}{8},\ ...$  

•  $c_n=1,\ \frac{1}{2},\ \frac{1}{3},\ \frac{1}{4},\ ...$  

•  $d_n=\ 1,\ 0.95,\ 0.90,\ 0.85,\ ...$  

For another geometric sequence

 $e_n=-6,\ 3,\ -\frac{3}{2},\ \frac{3}{4},\ ...$  write down the common ratio. (Type the value only, example: if r = 4 type 4 or if r = 1/3 type 1/3)

(a)  

For another arithmetic sequence

 $f_n=-4,\ -3.5,\ -3,\ -2.5,\ -2,\ ...$  write down the common difference. (Type the value only, example: if d = 4 type 4)

(a)  

A new cafe opened and during the first week their profit was $60. The cafe's profit increases by $10 every week.

Find the cafe's profit during the 11th week. (Type the value only. Example: $45 should be typed as 45)

(a)  

A new cafe opened and during the first week their profit was $60. The cafe's profit increases by $10 every week.

Calculate the cafe's total profit for the first 12 weeks. (Type the value only. Example: $45 should be typed as 45)

(a)  

A new tea-shop opened at the same time as the cafe. During the first week their profit was also $60. The tea-shop's profit increases by 10% every week.

Find the tea-shop's profit during the 11th week in 3 SF. (Type the value only, example: $18 should be typed as 18).

(a)  

A new tea-shop opened at the same time as the cafe. During the first week their profit was also $60. The tea-shop's profit increases by 10% every week.

Calculate the tea-shop's total profit for the first 12 weeks in 3 SF. (Type the value only, example: $18 should be typed as 18).

(a)  

The first term of an arithmetic sequence is 3 and the sum of the first two terms is 11.

Write down the second term of this sequence.

(a)  

The first term of an arithmetic sequence is 3 and the sum of the first two terms is 11.

Write down the common difference of this sequence.

(a)