Find a and d for the following arithmetic progression: 12, 12.5, 13, 13.5, ...
a=12.5 d=0.5
100
Find the value of x if this set of numbers forms an arithmetic sequence: 32 , x , 14
23
100
Write the next 3 terms of the following geometric progression: 81, 27 , 9 , ...
3, 1, 1/3
100
Find the limiting sum of the series -4 , -2 , -1 , ...
-8
100
Globa earned $25 000 in her first year of work, and her salary increased every year by $3000 for 12 years. Find her salary in the 12th year.
$58 000
200
Evaluate the 35th term of the following arithmetic series: 7 + 12 + 17 + ...
177
200
Find the 9th term and the 100th term of the sequence: 6 , 16 , 26 , ...
9th term = 86 100th term = 996
200
Find the 14th term of the following geometric series: 0.04 , 0.2 , 1 , ...
48 828 125
200
How many terms are in this finite sequence? -1 , -3 , -9 , ... , -81
5 terms
200
Find the common ratio of the series 100 + 101 + 102.01 + ... and find the sum of the first 20 terms of the series to 2dp.
r = 1.01 Sum = 2201.90 (2dp)
300
Find the 20th term and hence the sum of the first 20 terms of the following series: 15 + 9 + 3 + ...
Term 20=-99 Sum = -840
300
For the sequence 2 , 5 , 8 , ... which term has the value 2000?
667th
300
Find the common ratio for the following geometric progression and find its 6th term
r=-6 Term 6=-486
300
The first term of a geometric series is 3 and the 6th term is 96. Find the value of the 10th term
1536
300
The third term of an Arithmetic Progression is 16 and the 12th term is 79. Find the 41st term.
282
400
Evaluate the sum 600-2n (n=0-175)
74800 (there are 176 terms as n starts at 0)
400
Find the first term and common difference of the arithmetic progression with 10th term = 18 and 20th term = 48
d=3 a=-9
400
The nth term of a geometric sequence is given by the equation 25 x 2^n. Which term of the sequence is 6400?
8th term
400
Write 0.272727... as an infinite geometric progression.
Then find the limiting sum and express the recurring decimal as a fraction.
0.27+0.0027+0.000027+... = 3/11
400
The number of infections in an epidemic rose from 10 000 on 1st Jul to 160 000 on 1st of Sep. The increase is a constant ratio each month, how many infections on 1st August?
40 000
500
Evaluate x if the following is an arithmetic progression: x-3, 5 , 2x+7 . Hence evaluate the 3 terms.
x=2 First 3 terms: -1, 5, 11
500
Logs of wood are stacked with 10 on the top row, 11 on the next, and so on. If there are 390 logs, find the number of rows and the number of logs on the bottom row.
20 rows 29 logs on bottom row
500
Find the number of terms that sum to -425 in the series 5 - 10 + 20 + ...
8 terms
500
Bevin dropped a ball from a height of 8 metres. It bounced continually, each succesive height being half of the previous height. Through what distance did the ball 'eventually' travel?
4/0.5=8 8x2=16 16+8= 24 metres
500
In its first year a business has sales of $200 000, and each year sales increase by 20%. In which year do total sales since foundation first exceed $2 000 000