*Give answers in the form $u_n=an+b$ where $a$ and $b$ are numbers
Is the sequence $3,6,9,12,15,...$ arithmetic, geometric, or neither?
Find a formula for the general term of $3,6,9,12,15,...\qquad u_n=$
Find a formula for the general term of $4,7,10,13,16,...\qquad u_n=$
Find a formula for the general term of $5,8,11,14,17,...\qquad u_n=$
Find a formula for the general term of $6,9,12,15,18,...\qquad u_n=$
Find a formula for the general term of $10,13,16,19,22,...\qquad u_n=$
Find a formula for the general term of $100,103,106,109,112,...\qquad u_n=$
Find a formula for the general term of $2,5,8,11,14...\qquad u_n=$
Find a formula for the general term of $1,4,7,10,13,...\qquad u_n=$
Find a formula for the general term of $0,3,6,9,12,...\qquad u_n=$
Find a formula for the general term of $-1,2,5,8,11,...\qquad u_n=$
Find a formula for the general term of $-100,-97,-94,-91,-88,...\qquad u_n=$
General Term of Arithmetic Sequences
Find the general term, $u_n$, for the following sequences.
*Write your answers in the form $an+b$ where $a$ and $b$ are numbers.
Also, find the 100th term, $u_{100}$
$1,3,5,7,9,\ldots \qquad u_n=$
$u_{100}=$
$15,18,21,24,27,\ldots \qquad u_n=$
$u_{100}=$
$6,17,28,39,50,\ldots \qquad u_n=$
$u_{100}=$
$-11,-14,-17,-20,-23,\ldots \qquad u_n=$
$u_{100}=$
$13,5,-3,-11,-19,\ldots \qquad u_n=$
$u_{100}=$
*Write your answer in the form $\frac{\boxed{\phantom{1}}}{\boxed{\phantom{3}}}n+\frac{\boxed{\phantom{1}}}{\boxed{\phantom{6}}}:\qquad$ $\frac{1}{2},\frac{5}{6},\frac{7}{6},\frac{3}{2},\frac{11}{6},\ldots \qquad u_n=$
$u_{100}=$
The $n^{th}$ Term of an Arithmetic Sequence
For arithmetic sequences, the number that is added each time to find the next term is called the
.
It is usually denoted by the letter
.
$$u_1\overset{+d}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_2}{\text{___}}\overset{+d}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_3}{\text{___}}\overset{+d}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_4}{\text{___}}\overset{+d}{\overset{\Huge\frown}{\phantom{A},\phantom{B}}}\underset{u_5}{\text{___}}\phantom{A},\quad\ldots$$
Let's find the terms of an arithmetic sequence starting from $u_1$:
$\qquad u_2 = u_1+d$
$\qquad u_3 = u_1+d+d$
$\qquad u_4 = u_1+d+d+d$
Follow this pattern and express $u_5$ and $u_6$ in terms of $u_1$ and $d$
$\qquad u_5 = $
$\qquad u_6 = $
To find $u_n$, how many $d$'s must be added to $u_1$?
For arithmetic sequences, $u_n=u_1+($
$)\times d$.
Consider the sequence $2, 9, 16, 23, 30, …$
a)
b)
c)
d)
Find $k$ given that $3k+1, k$, and $-3$ are consecutive terms of an arithmetic sequence.
Find the general term $u_n$ for an arithmetic sequence with $u_3=8$ and $u_8=-17$.
Write down all six terms of an arithmetic sequence with $u_1=3$ and $u_6=12$. Separate the terms with commas.