Arithmetic Sequences
Arithmetic Series and Sigma Notation
Arithmetic Sequences and Series Word Problems
Geometric Sequences
Geometric Series ( Finite and Infinite)
100
Is the given sequence arithmetic? If so, what is the value of D ?
-34 , -30 , -26 , -22 , -18 , -14 ...
Yes
4
100
Find the sum for the given sequence.
Given : 7n+4
Find : S5
S5 = 125
100
A drive-in theater has spaces for 25 cars in the first row, 30 in the second row, 35 in the third row and so on. If there are 19 rows, how many cars can be parked?
Formula : Sn = n/2 (a1 + an)
Formula : an = a1 + d(n-1)
Sn = 1330
100
Is the given sequence geometric ? If so, what is the value of r ?
224 , 56 , 14 , 3.5 ...
Yes
1/4
100
Find the sum of the finite series.
a1 = 7 r = 6 n = 9
Formula : Sn = a1(1-rn)/(1-r)
Sn = 14,108,773
200
Find the a35 for the sequence.
23 , 36 , 49 , 62 , 75 ...
Formula : an=a1+d(n-1)
a35 = 465
200
Find the sum of the given sequence
Given : 7(13n+4)
Find : S3
S3 = 630
200
The purchase value for a car was $97,000. The value of the car decreases after ten years was $83,500. What was the annual depreciation value ?
Formula : an = a1 + d(n-1)
D = $1500
200
a1 = 19 r= 6 Find the 11th term.
Formula : an = a1(r)n-1
a11 = 1,148,857,344
200
The first term is -4 and the common ratio is 8. How many terms were added together to make -18724?
Formula : Sn = a1(1-rn)/(1-r)
n = 5
300
What is the common difference for the sequence where the first term is 4 and the 6th term is 129 ?
Formula : an=a1+d(n-1)
D = 25
300
Find the sum of each arithmetic series.
a1 = 15 d = -6 n = 18
Formula : Sn = n/2 (a1 + an)
Sn = -648
300
A can display has 14 cans on the fourth row and 42 can on the eleventh row. How many cans were on the first row?
Formula : an = a1 + d(n-1)
a1 = 2
300
Which term is 295,245 in the sequence of
5 , 15 , 45 , 135 ...
Formula : an = a1(r)n-1
n = 11
300
Determine if each series converges or diverges. If it converges, find the sum.
S = 6
400
The 39th term in a sequence is 271. The 28th term in a sequence is 216. What is the 19th term ?
Formula : an=a1+d(n-1)
a19 = 171
400
What is the 4th term in an arithmetic series if the first term is 13 , the nth term is 61 and the sum is 259 ?
Formula : Sn = n/2 (a1 + an)
Formula : an = a1 + d(n-1)
n = 37
400
A child on a swing is given a big push. She travels 16 feet on the first swing but 3/8 as far on each sucessive swing. How far in total distance did she travel before she stopped?
Formula : S = a1/(1-r)
S = 25.6
400
Find the four missing terms in the geometric sequence.
-12 , ___ , ___ , ___ , ____ , -37500
Formula : an = a1(r)n-1
-60
-300
-1500
-7500
400
The first term is an infinite series is 81 and its sum is 324. What is the common ratio?
Formula : S = a1/(1-r)
r = .75 or 3/4
500
Find the missing terms in the arithmetic
sequence
126 , ____ , _____ , 105 .....
Formula : an=a1+d(n-1)
119 , 112
500
Evaluate the seires.
Sn = -1056
500
A three ton ice sculpture is melting 65% of its original weight per hour. How much of the sculpture in pounds will be left after 8 hours?
Formula : an = a1(r)n-1
a8 = 3.860
500
a1 = 8 r = 12 Find the seventh term.
Formula : an = a1(r)n-1
a7 = 23,887,872
500
A banana slug crawls 4 inches on one day. On each successive day the distance it crawls decreases by 2%. If this pattern continues indefinitely, how far will the slug crawl all together.
Formula : Sn = a1/(1-r)
200 inches