Sequence
Determine the first term of the arithmetic sequence in which the 16th term is 110 and the common difference is 7.
What is 5
Find S10 for the following series,
10+7+4+...
What is S10=-35
True or False
Is the term 89 part of the following sequence:
tn=107-3n ?
What is true?
Suppose the color of jeans fades by 5% (meaning that 95% remains) each time they are washed. What percent of the original color remains in the jeans after 27 washes? (Hint: go to the 28th term. The first term is 100% or 1.)
What is 25% ?
Determine whether the following infinite geometric series is convergent or divergent
0.1+0.05+0.025+0.0125+...
What is convergent?
Expand (n+4)2 .
What is n2+8n+16 ?
It's About Time in Langley, British Columbia is Canada's largest custom clock manufacturer. They have a grandfather clock that, on hours, chimes the number of hours that corresponds to the time of day. How many times does the clock chime in 24 hrs?
What is 156 times?
(78 is sum for first 12 hours, doubled would be 156)
Determine the value of n for the given value.
-19,-13,-7,..., 119
What is n=24?
A persons kidney filters out 18% of a particular medicine every two hours (keeping 82%). How much medicine remains after 12 hrs if the initial dosage was 250mL. This means that we are looking for the 7th term!
What is 76.0ml?
Determine the sum of the infinite geometric series
2+2(0.6)+2(0.6)2+2(0.6)3+...
What is 5?
Determine the formula for the nth term of the of the geometric sequence.
192,-48,12,-3,...
What is An=192(-1/4)n-1
Expand (v-2)3?
What is v3-6v2+12v-8?
The sum of the first nine terms of an arithmetic series is 162, and the first term is 2. Determine the next four terms.
What is 2+6+10+14+18 ?
The coefficient of x in the expansion of (x+3)5.
What is 405?
If the first term of an infinite geometric series is -18 and the sum is -45 then what is the common ratio?
What is r= 3/5 or 0.6?
The population of a city increases by 6.5% each year. If the initial population is 200,000, what is the population after 30 years (n=31)?
What is 1,322,873?
What is 15
Expand completely (2m-1)4.
What is 16m4-32m3+24m2-8m+1 ?
A doctor prescribes 200mg of medication on the first day of treatment. The dosage is reduced by one half on each successive day for one week (7 days). What is the total amount of medication prescribed?
What is 397mg?
The sum of an infinite series is 120 and the common ratio is -2/5 or -0.4. Then What is A1?
What is A1= 168?
If 25, 62.5, 156.25 are three consecutive terms in a geometric sequence, determine the value of the common ratio?
What is r=5/2?
What is the sum of the 8 terms in the geometric series
4+16+64+...+65,536 ?
What is S8=87,380 ?
Determine S30 for the following series.
5+5.3+5.6+...
What is S30=280.5?
If every person has two parents, four grandparents, eight great-grandparents, and so on. Determine the number of ancestors a person has back through ten generations. (Hint: first term should be 2)
What is S10=2046?
The length of an initial swing of a pendulum is 90cm. Each successive swing is 0.7 times the length of the previous swing. If the process continues forever, how far will the pendulum swing?
What is 300 cm?