Arithmetic Sequences
What is the 52nd term of the arithmetic sequence whose first term is 36 and whose common difference is -100?
-5064
Find the tenth term of the geometric sequence whose first term is -2 and common ratio is 4.
-524288
Evaluate:
sum_(k = 1)^5 (3k-13)
-20
Evaluate:
sum_(i = 1)^9 3^(i - 1)
9841
Each day, Mrs. G.A. exercises 10 minutes her first day of her new exercise routine. Each day she exercises 2 more minutes than the day before. How many minutes does she exercise on day 25? Don't forget to include units!
58 minutes
Write the explicit rule for the arithmetic sequence whose common difference is 10 and
a_30 = 327
a_n = 10n + 27
Write the explicit rule for the geometric sequence whose common ratio is -3 and
a_5 = 324
a_n = 4(-3)^(n-1)
Evaluate:
sum_(i = 1)^20 (-4i-2)
-880
The first term of a geometric series is 2 and the common ratio is -3. Find the sum of the first 10 terms of the series.
-29524
The first day a restaurant opens, it gets 5 customers. But each day, the number of customers doubles from the day before. How many customers does the restaurant get on the 10th day it is open? Please include units!
2560 customers
Write a rule of the sequence:
10, 15/2, 5, 5/2, ...
a_n = -5/2n + 25/2
Write the rule for the following sequence:
9, -6, 4, -8/3, ...
a_n = 9(-2/3)^(n-1)
The first term of an arithmetic series is -4 and the common difference is 5. Find the sum of the first 20 terms of that series.
870
Find the sum of the first eight terms of the series:
3 + 12 + 48 + 192 + ...
65535
In a triangular formation of gooses, the first row has one goose, and each consecutive row has two more geese than the row before. How many geese are in the formation, total, if there are 22 rows? Make sure to include units!
484 geese
Create the rule for the arithmetic sequence where
a_17 = -305 and a_32 = -605
a_n = -20n + 35
Write the explicit rule of the geometric sequence whose sixth term is -729 and whose third term is 27.
a_n = 3(-3)^(n-1)
Find the sum of the first 10 terms of the series.
-14 - 20 - 26 - 32 - ...
-410
Find the infinite sum of the series, if possible.
-7.5 - 3.75 - 1.875 - 0.9375 - ...
-15
Mrs. G.A.'s grading feels never-ending. The first day, she grades for 75 minutes, and each consecutive day she grades 35% less time than the day before infinitely. How many minutes of grading does Mrs. G.A. do? Round to the nearest tenth and don't forget units!
214.3 minutes
What is the 75th term of the arithmetic sequence whose 19th term is -125 and 35th term is -237?
-517
Find the ninth term of the geometric sequence given
a_3 = -48 and a_6 = -3072
-196608
Write the expression, using sigma notation, of the sum of the first 19 terms of the following series. Then, find that sum.
17+22+27+32+...
sum_(n= 1)^19(5n + 12)
S_19 = 1178
Write the expression, using sigma notation, of the sum of the first 8 terms of the following series. Then, find that sum.
-4 + 12 - 36 + 108 - ...
sum_(n = 1)^8 -4(-3)^(n-1)
S_8 = 6560
Each year, Mrs. G.A. deposits 7% less into her daughter's college saving account. The first year, she deposited $12,000. How much money will be in the account if the contributes money for 18 years? Round appropriately for money.
$125,000.97