Sequences and Series Review Y11 IB HL

find the sum of the following infinite geometric sequence:

$18\ ,\ -12\ ,\ +8,\ ...$

• $10\ \frac{4}{5}$

• 1

• 0

• - 10.8

find the nth term of an arithmetic sequence with

 $u_7=31\ \ \ \ \ and\ \ \ \ \ \ \ u_{15}=\ -\ 17$  

•  $u_n=-\ 6n\ +\ 17$  

•  $u_n=-\ 6n$  

•  $u_n=\ 73\ -\ 6n$  

•  $u_n=\ -6n\ -173\$  

find the sum of the first 12 terms of the sequence:

 $3,\ 9,\ 15,\ 21,\ ...$  

•  $\infty$  

• 432

• - 234

• 396

find the first term of the sequence :

 $5,\ 10,\ 20,\ 40,\ ...$  that exceeds 10000.

•  $u_{13}$  

•  $u_{110}$  

•  $u_{11}$  

•  $u_{12}$  

Margaret invests 5000$ at a rate of 5.8% p.a compounded monthly. Use technology to find how long it will take to amount to 12000$.

• almost 15 years

• 182 months

• 181 months

• 15 years and a bit

• 15.7 years

A car was bought for 9800$ in 2019. According to the market, it will depreciate by 26% each year. Find what is going to be its value in 2024.

• 2174.63 $

• 2173.64 $

• 2176 $

• 2175.67 $

select the FALSE statement:

• arithmetic sequences are completely determined by their first term and common difference.

• all geometric sequences with r > 1 are convergent to a finite number.

• the sum to infinity of an arithmetic sequence is, of course, infinite.

• Geometric sequences are completely defined by their first term and their common ration.

The sum of an infinite geometric series is 49, and the second term of the series is 10. find the possible values for the sum of the first 3 terms of the series.

• -7,857 and -3.43

• 3447,7 and 139.3

• 77,57 and -1.143

• 47,857 and 31.143

In 1988 there were 3000 rabbits in a farm. Since then, the population of rabbits has increased by 5% each year. How many rabbits there were in 1991?

• 3469 rabbits.

• 3471 rabbits.

• 3470 rabbits.

• 3470.5 rabbits.

a ball is dropped vertically from  $2\ m$  in the air. Each time it bounces up to a height of 80% of its previous height. How far has it travelled when it hits the ground for the

 $9^{th}$  time?

• 10,85 m

• 0.85 m

• 15,85 m

• 15 m