In an arithmetic sequence, each term is found by adding or subtracting the same number to the previous term.
In a geometric sequence, each term is found by multiplying or dividing the same number to the previous term.
For each of the following sequences, identify if it is an “arithmetic” or “geometric” sequence or “neither”.
a)For the sequence $7,14,21,28,35,...$, what number is added each time to get the next term?
b)Find a formula for the general term of $7,14,21,28,35,...\qquad u_n=$
c)Find a formula for the general term of $8,15,22,29,36,...\qquad u_n=$
d)Find a formula for the general term of $3,10,17,24,31,...\qquad u_n=$
e)Find a formula for the general term of $50,57,64,71,78,...\qquad u_n=$
f)Find a formula for the general term of $-7,-14,-21,-28,-35...\qquad u_n=$
g)Find a formula for the general term of $-8,-15,-22,-29,-36...\qquad u_n=$
h)Find a formula for the general term of $0,-7,-14,-21,-28,-35...\qquad u_n=$
i)Find a formula for the general term of $18,11,4,-3,-10,...\qquad u_n=$
j)Find a formula for the general term of $-100,-107,-114,-121,-128...\qquad u_n=$
General Term of Arithmetic Sequences
Find the general term, $u_n$, for the following sequences.
*Write your answers in the form $an+b$ where $a,b$ are numbers.
a)$1,3,5,7,9,\ldots \qquad u_n=$
b)$15,18,21,24,27,\ldots \qquad u_n=$
c)$6,17,28,39,50,\ldots \qquad u_n=$
d)$13,5,-3,-11,-19,\ldots \qquad u_n=$
e)$-11,-14,-17,-20,-23,\ldots \qquad u_n=$
f)*Write your answer in the form $\frac{\boxed{\phantom{1}}}{\boxed{\phantom{3}}}n+\frac{\boxed{\phantom{1}}}{\boxed{\phantom{6}}}:$ $\frac{1}{2},\frac{5}{6},\frac{7}{6},\frac{3}{2},\frac{11}{6},\ldots \qquad u_n=$
Exercises
(26B on P.537) #1cfi, #2cf, #4, #5, #6 right column, #7, #8