# Sequences & Series Questions and Answers

Math

Sequences & SeriesWrite the first six terms of the arithmetic sequence with the first term, a₁, and common difference, d.
a₁ = 4, d = 1
a2
a3
24
=
a5 = 0
86 = 0
a6
...

Math

Sequences & SeriesDetermine whether the sequence is arithmetic or geometric. Then find the next two terms.
1/2, 1, 3/2, 2..
Determine whether the sequence is arithmetic or geometric. Choose the correct answer below.
Geometric
Arithmetic
2,..
Write next two terms.
1/2, 1, 3/2, 2..

Math

Sequences & SeriesFor each arithmetic series described below, write the series and calculate its sum. If it is not possible, explain why not.
a. You know that the first term is 18, the last term is 72, and the common difference is 4.5. What is the series? What is the sum?
b. You know that the series has nine terms and the last term is 18. What is the series? What is the sum?
c. You know that the third term of an 18-term series is 29 and the terms are increasing by 10. What is the series? What is the sum?

Math

Sequences & SeriesRosurvastatin/Crestor is a medicine used to decrease bad cholesterol and increase good cholesterol in the body. The half-life of Rosurvastatin is 1 day, which means that at the end of 1 day, half as much of the medication is left in your system. 1. If you take 60 mg of Rosurvastatin, how long do you think will it stay in your system?

Math

Sequences & SeriesFind a formula for the nº partial sum of the series series converges.
The formula for the n
A. The series converges. The series' sum is
B. The series diverges.
If the series converges, what is the series' sum? Select the correct choice below and fill in any answer boxes within your choice.

Math

Sequences & Series11. (a) Write the first 5 terms of a power series approximation for f(x) = e-x*² centered at
X = 0.
(b) Use the above power series approximation to find an approximation to S₁¹₁e-x² dx,
rounding to 3 decimal places. Show work needed to produce this approximation.
(c) Include a graph, shade the region corresponding to the integration and confirm your
answer above using the computer or calculator to evaluate the integral.

Math

Sequences & SeriesThe real number 0.9 can be written as an infinite series as shown below:
(a) Write the infinite series in sigma notation and use the formula for the sum of a
infinite geometric series to find the sum.
(b) Write the exact value of the infinite sum (not as a repeating decimal).

Math

Sequences & SeriesA bottle contains 95 milliliters of lemon extract solution. If. the extract contains 25 milliliters of alcohol, what is the volume percent (v/v) of the alcohol in the solution? Make sure to include a correct unit symbol with the answer choice.

Math

Sequences & SeriesDetermine whether the following statement is true or false, and explain why.
In a Markov chain, the outcome of an experiment depends only on the present state and not on any past states.
Is the statement true or false?
A. True.
B. False. In a Markov chain, the outcome of an experiment depends on past states found using transition matrice
C. False. In a Markov chain, the outcome of an experiment depends on past states found using probability vector
D. False. In a Markov chain, the outcome of an experiment depends on both past and present states.

Math

Sequences & SeriesWrite the first five terms of the sequence whose general term, an, is given as
an=-5n+ 8.

Math

Sequences & SeriesWrite the terms of 4Σi=1 f(xi) Δx., with x₁ = 2, X₂ = 6, x3 = 4, x4 = 0, and Ax=0.2, for the function f(x) =-5/x+1
What is the first term in the series?
a₁ = (Simplify your answer. Type an integer or a simplified fraction.)
Evaluate the sum.

Math

Sequences & SeriesFind the missing terms of the sequence and determine if the sequence is arithmetic, geometric, or neither.
6, 11, 16, 21,_______,______ .

Math

Sequences & SeriesWrite the terms for the series. Evaluate the sum, given that x₁ =-2, X₂ = -1, x3 =0, x4=1, and x5 = 2.
5
Σ (-3x₁)
i=1
The first term is __.
The second term is __.
The third term is __.
The fourth term is __.
The fifth term is __.
5
Σ (-3x₁)=
i=1

Math

Sequences & SeriesWrite the terms of 4Σi=1 f(x1) Δx with x₁ = 0, x₂ = 2, x3 = 4, x4= 6, and Δx=1.5, for the function f(x) = 7x². Evaluate the sum.
What is the first term in the series?
a₁ = (Simplify your answer. Type an integer or a simplified fraction.)

Math

Sequences & SeriesA painting sold for $277 in 1978 and was sold again in 1990 for $485. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V₂ = 277.
k=_
(Round to the nearest thousandth.)
b) Find the exponential growth function in terms of t, where t is the number of years since 1978.
V(t)=_
c) Estimate the value of the painting in 2015.
$_
(Round to the nearest dollar.)
d) What is the doubling time for the value of the painting to the nearest tenth of a year?
_years
(Round to the nearest tenth.)
e) Find the amount of time after which the value of the painting will be $2173.
_years
(Round to the nearest tenth.)