# 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.

what is math number
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
An investment account was opened with an initial deposit of \$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar