# 9.2 Arithmetic sequences  (Page 5/8)

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What are the main differences between using a recursive formula and using an explicit formula to describe an arithmetic sequence?

Describe how linear functions and arithmetic sequences are similar. How are they different?

Both arithmetic sequences and linear functions have a constant rate of change. They are different because their domains are not the same; linear functions are defined for all real numbers, and arithmetic sequences are defined for natural numbers or a subset of the natural numbers.

## Algebraic

For the following exercises, find the common difference for the arithmetic sequence provided.

$\left\{5,11,17,23,29,...\right\}$

$\left\{0,\frac{1}{2},1,\frac{3}{2},2,...\right\}$

The common difference is $\frac{1}{2}$

For the following exercises, determine whether the sequence is arithmetic. If so find the common difference.

$\left\{11.4,9.3,7.2,5.1,3,...\right\}$

$\left\{4,16,64,256,1024,...\right\}$

The sequence is not arithmetic because $16-4\ne 64-16.$

For the following exercises, write the first five terms of the arithmetic sequence given the first term and common difference.

${a}_{1}=-25$ , $d=-9$

${a}_{1}=0$ , $d=\frac{2}{3}$

$0,\text{\hspace{0.17em}}\frac{2}{3},\text{\hspace{0.17em}}\frac{4}{3},\text{\hspace{0.17em}}2,\text{\hspace{0.17em}}\frac{8}{3}$

For the following exercises, write the first five terms of the arithmetic series given two terms.

${a}_{1}=17,\text{\hspace{0.17em}}{a}_{7}=-31$

${a}_{13}=-60,\text{\hspace{0.17em}}{a}_{33}=-160$

$0,-5,-10,-15,-20$

For the following exercises, find the specified term for the arithmetic sequence given the first term and common difference.

First term is 3, common difference is 4, find the 5 th term.

First term is 4, common difference is 5, find the 4 th term.

${a}_{4}=19$

First term is 5, common difference is 6, find the 8 th term.

First term is 6, common difference is 7, find the 6 th term.

${a}_{6}=41$

First term is 7, common difference is 8, find the 7 th term.

For the following exercises, find the first term given two terms from an arithmetic sequence.

Find the first term or ${a}_{1}$ of an arithmetic sequence if ${a}_{6}=12$ and ${a}_{14}=28.$

${a}_{1}=2$

Find the first term or ${a}_{1}$ of an arithmetic sequence if ${a}_{7}=21$ and ${a}_{15}=42.\text{\hspace{0.17em}}$

Find the first term or ${a}_{1}$ of an arithmetic sequence if ${a}_{8}=40$ and ${a}_{23}=115.$

${a}_{1}=5$

Find the first term or ${a}_{1}$ of an arithmetic sequence if ${a}_{9}=54$ and ${a}_{17}=102.$

Find the first term or ${a}_{1}$ of an arithmetic sequence if ${a}_{11}=11$ and ${a}_{21}=16.$

${a}_{1}=6$

For the following exercises, find the specified term given two terms from an arithmetic sequence.

${a}_{1}=33\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}{a}_{7}=-15.$ Find $\text{\hspace{0.17em}}{a}_{4}.$

${a}_{3}=-17.1\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}{a}_{10}=-15.7.$ Find ${a}_{21}.$

${a}_{21}=-13.5$

For the following exercises, use the recursive formula to write the first five terms of the arithmetic sequence.

$-19,-20.4,-21.8,-23.2,-24.6$

For the following exercises, write a recursive formula for each arithmetic sequence.

${a}_{n}=\left\{40,60,80,...\right\}$

${a}_{n}=\left\{17,26,35,...\right\}$

${a}_{n}=\left\{-1,2,5,...\right\}$

${a}_{n}=\left\{12,17,22,...\right\}$

${a}_{n}=\left\{-15,-7,1,...\right\}$

${a}_{n}=\left\{8.9,10.3,11.7,...\right\}$

${a}_{n}=\left\{-0.52,-1.02,-1.52,...\right\}$

${a}_{n}=\left\{\frac{1}{5},\frac{9}{20},\frac{7}{10},...\right\}$

${a}_{n}=\left\{-\frac{1}{2},-\frac{5}{4},-2,...\right\}$

${a}_{n}=\left\{\frac{1}{6},-\frac{11}{12},-2,...\right\}$

For the following exercises, write a recursive formula for the given arithmetic sequence, and then find the specified term.

Find the 17 th term.

Find the 14 th term.

Find the 12 th term.

show that the set of all natural number form semi group under the composition of addition
explain and give four Example hyperbolic function
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Abdullahi
hi mam
Mark
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak