Given the first term and the common difference of an arithmetic sequence, find the first several terms.
Add the common difference to the first term to find the second term.
Add the common difference to the second term to find the third term.
Continue until all of the desired terms are identified.
Write the terms separated by commas within brackets.
Writing terms of arithmetic sequences
Write the first five terms of the
arithmetic sequence with
${a}_{1}=17$ and
$d=-3$ .
Adding
$\text{\hspace{0.17em}}-3\text{\hspace{0.17em}}$ is the same as subtracting 3. Beginning with the first term, subtract 3 from each term to find the next term.
The first five terms are
$\text{\hspace{0.17em}}\{17,\text{\hspace{0.17em}}14,\text{\hspace{0.17em}}11,\text{\hspace{0.17em}}8,\text{\hspace{0.17em}}5\}$
Given any the first term and any other term in an arithmetic sequence, find a given term.
Substitute the values given for
${a}_{1},{a}_{n},n$ into the formula
$\text{\hspace{0.17em}}{a}_{n}={a}_{1}+(n-1)d\text{\hspace{0.17em}}$ to solve for
$\text{\hspace{0.17em}}d.$
Find a given term by substituting the appropriate values for
$\text{\hspace{0.17em}}{a}_{1},n,\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}d\text{\hspace{0.17em}}$ into the formula
${a}_{n}={a}_{1}+(n-1)d.$
Writing terms of arithmetic sequences
Given
${a}_{1}=8$ and
${a}_{4}=14$ , find
${a}_{5}$ .
The sequence can be written in terms of the initial term 8 and the common difference
$d$ .
$$\left\{8,8+d,8+2d,8+3d\right\}$$
We know the fourth term equals 14; we know the fourth term has the form
${a}_{1}+3d=8+3d$ .
Some arithmetic sequences are defined in terms of the previous term using a
recursive formula . The formula provides an algebraic rule for determining the terms of the sequence. A recursive formula allows us to find any term of an arithmetic sequence using a function of the preceding term. Each term is the sum of the previous term and the common difference. For example, if the common difference is 5, then each term is the previous term plus 5. As with any recursive formula, the first term must be given.
Do we have to subtract the first term from the second term to find the common difference?
No. We can subtract any term in the sequence from the subsequent term. It is, however, most common to subtract the first term from the second term because it is often the easiest method of finding the common difference.
A cell phone company offers two plans for minutes. Plan A: $15 per month and $2 for every 300 texts. Plan B: $25 per month and $0.50 for every 100 texts. How many texts would you need to send per month for plan B to save you money?
Hey I am new to precalculus, and wanted clarification please on what sine is as I am floored by the terms in this app? I don't mean to sound stupid but I have only completed up to college algebra.
I don't know if you are looking for a deeper answer or not, but the sine of an angle in a right triangle is the length of the opposite side to the angle in question divided by the length of the hypotenuse of said triangle.
Marco
can you give me sir tips to quickly understand precalculus. Im new too in that topic.
Thanks
Jenica
if you remember sine, cosine, and tangent from geometry, all the relationships are the same but they use x y and r instead (x is adjacent, y is opposite, and r is hypotenuse).
Natalie
it is better to use unit circle than triangle .triangle is only used for acute angles but you can begin with. Download any application named"unit circle" you find in it all you need. unit circle is a circle centred at origine (0;0) with radius r= 1.
SLIMANE
What is domain
johnphilip
the standard equation
of the ellipse that has vertices (0,-4)&(0,4) and foci (0, -15)&(0,15)
it's standard equation is x^2 + y^2/16 =1
tell my why is it only x^2? why is there no a^2?
This term is plural for a focus, it is used for conic sections. For more detail or other math questions. I recommend researching on "Khan academy" or watching "The Organic Chemistry Tutor" YouTube channel.
Chris
how to determine the vertex,focus,directrix and axis of symmetry of the parabola by equations
For each year t, the population of a forest of trees is represented by the function A(t) = 117(1.029)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 86(1.025)t.