# Infinite Sequences

### Topic Page

Infinite Sequences### Questions

- What is a sequence?
- How does the Fibonacci sequence relate to Pascal's triangle?
- What is the Fibonacci sequence?
- How do I find the #n#th term of the Fibonacci sequence?
- How do you find the general term for a sequence?
- How do find the #n#th term in a sequence?
- What is the golden ratio?
- How does the golden ratio relate to the Fibonacci sequence?
- How do you determine if -10,20,-40,80 is an arithmetic or geometric sequence?
- How do you determine if 15,-5,-25,-45 is an arithmetic or geometric sequence?
- A man went to his bank and deposited $1,663. A couple of days later, that same man deposited $1,527. A few days after that, he deposited $1,126. A couple days later, he deposited $1,096. What was his next deposit?
- What is the next number in the sequence 72, 36, 18, ____, 4.5?
- What is the next number in the sequence 625, 25, ____?
- What is the next number in the sequence ___, ____, 16,256, 65,536?
- What is the next number in the sequence ___, ___, 16, 25, 36?
- What is the next number in this sequence 1, 1, 3, 2, 4, 6, 5, 25?
- What is the pattern in the sequence 1, 3, 4, 7, 6, 12, 8, 15, 13, ??
- What is the pattern in the sequence 100, 19, 83, 34, 70, 45?
- What is the pattern in the sequence 1, 1, 0, -1, 0, 7, 28, 79, 192?
- What is the pattern in the sequence 2, 5, 10, 17, 28, 41, 58, 77, 100?
- What is the pattern in the sequence 1 2 4 3 6 8 7 14 16?
- How do you find the sum of the first 25 terms of an arithmetic sequence whose 7th term is −247 and whose 18th term is −49?
- For the sequence an = 4n + 5 how do you find the first five terms?
- What is the formula for the sequence #2, -1, 4, -7, 10, -13, 16,...# ?
- The sequence #0, 2, 8, 30, 112, 418,...# is defined recursively by #a_0 = 0#, #a_1 = 2#, #a_(n+1) = 4a_n-a_(n-1)#. What is the formula for a general term #a_n#?
- How do you write a recursive formula for a sequence whose first three terms are 1, 1, and 3?
- How do you find the first five terms of each sequence #a_1=12#, #a_(n+1)=a_n-3#?
- How do you find the first five terms of each sequence #a_1=-3#, #a_(n+1)=a_n+n#?
- How do you find the first five terms of each sequence #a_1=0#, #a_(n+1)=-2a_n-4#?
- How do you find the first five terms of each sequence #a_1=1#, #a_2=2# #a_(n+2)=4(a_(n+1))-3a_n#?
- How do you find the first three iterates for the function #f(x)=3x-4# given the initial value #x_0=3#?
- How do you find the first three iterates for the function #f(x)=-2x+5# given the initial value #x_0=2#?
- How do you find the first three iterates for the function #f(x)=x^2+2# given the initial value #x_0=-1#?
- How do you find the first five terms given #a_1=-6# and #a_(n+1)=a_n+3#?
- How do you find the first five terms given #a_1=13# and #a_(n+1)=a_n+5#?
- How do you find the first five terms given #a_1=2# and #a_(n+1)=a_n-n#?
- How do you find the first five terms given #a_1=6# and #a_(n+1)=a_n+n+3#?
- How do you find the first five terms given #a_1=9# and #a_(n+1)=2a_n-4#?
- How do you find the first five terms given #a_1=4# and #a_(n+1)=3a_n-6#?
- How do you find the first five terms given #a_1=-1#, #a_2=5#, #a_(n+1)=a_n+a_(n-1)#?
- How do you find the first five terms given #a_1=4#, #a_2=-3#, #a_(n+2)=a_(n+1)+2a_n#?
- How do you find the first five terms given #a_1=3/4#, #a_(n+1)=(n^2+1)/n*a_n#?
- If #a_0=7# and #a_(n+1)=a_n+12# for #n>=0#, how do you find the values of #a_5#?
- How do you find the first three iterate of the function #f(x)=9x-2# for the given initial value #x_0=2#?
- How do you find the first three iterate of the function #f(x)=4x-3# for the given initial value #x_0=2#?
- How do you find the first three iterate of the function #f(x)=3x+5# for the given initial value #x_0=-4#?
- How do you find the first three iterate of the function #f(x)=2x^2-5# for the given initial value #x_0=-1#?
- How do you find the first three iterate of the function #f(x)=3x^2-4# for the given initial value #x_0=1#?
- How do you find the first three iterate of the function #f(x)=3x^2-3x+2# for the given initial value #x_0=1/3#?
- If the rate of inflation is 2%, the cost of an item in future years can be found by iterating the function #c(x)=1.02x#, how do you find the cost of a $70 portable stereo in four years if the rate of inflation remains constant?
- How do you find the first five terms of the sequence #a_1=7#, #a_(n+1)=a_n-2#?
- How do you find the first five terms of the sequence #a_1=3#, #a_(n+1)=2a_n-1#?
- Apart from #2, 3# and #3, 5# is there any pair of consecutive Fibonacci numbers which are both prime?
- How do you express the sequence below as a recursively defined function 4, 11, 25, 53, 109,...?
- How do you find the nth term of the sequence #-1,2,-3,4,-5,6,...#?
- The nth term of a sequence is #2^n+2^(n-1)#, how do you work out the 10th term of the sequence?
- How do you identify #a_3# of this sequence: 0.25, 0.5, 0.75, 1, 1.25, 1.5,?
- How do you determine whether each sequence could be geometric, arithmetic, or neither. Use a patte to write the next three terms. 460, 46, 4.6, 0.46?
- What is the missing sequence in #1 3/8, 1 3/4, 2 1/8, __, 2 7/8#?
- Which of the following is the algebraic expression that best describes the sequence 7,14, 21, 28,?
- How do you write the first five terms of the sequence #a_n=3n+1#?
- How do you write the first five terms of the sequence #a_n=5n-3#?
- How do you write the first five terms of the sequence #a_n=2^n#?
- How do you write the first five terms of the sequence #a_n=(1/2)^n#?
- How do you write the first five terms of the sequence #a_n=(-1/2)^n#?
- How do you write the first five terms of the sequence #a_n=(n+2)/n#?
- How do you write the first five terms of the sequence #a_n=n/(n+2)#?
- How do you write the first five terms of the sequence #a_n=(6n)/(3n^2-1)#?
- How do you write the first five terms of the sequence #a_n=(3n^2-n+4)/(2n^2+1)#?
- How do you write the first five terms of the sequence #a_n=(1+(-1)^n)/n#?
- How do you write the first five terms of the sequence #a_n=1+(-1)^n#?
- How do you write the first five terms of the sequence #a_n=2-1/3^n#?
- How do you write the first five terms of the sequence #a_n=2^n/3^n#?
- How do you write the first five terms of the sequence #a_n=1/(n^(3/2))#?
- How do you write the first five terms of the sequence #a_n=10/n^(2/3)#?
- How do you write the first five terms of the sequence #a_n=3^n/(n!)#?
- How do you write the first five terms of the sequence #a_n=(n!)/n#?
- How do you write the first five terms of the sequence #a_n=(-1)^n(n/(n+1))#?
- How do you write the first five terms of the sequence #a_n=2/3#?
- How do you write the first five terms of the sequence #a_n=0.3#?
- How do you write the first five terms of the sequence #a_n=n(n-1)(n-2)#?
- How do you write the first five terms of the sequence #a_n=n(n^2-6)#?
- How do you find #a_25# given #a_n=(-1)^n(3n-2)#?
- How do you find #a_16# given #a_n=(-1)^(n-1)[n(n-1)]#?
- How do you find #a_10# given #a_n=2^n/(n!)#?
- How do you find #a_8# given #a_n=(n!)/(2n)#?
- How do you find #a_11# given #a_n=(4n)/(2n^2-3)#?
- How do you find #a_13# given #a_n=(4n^2-n+3)/(n(n-1)(n+2))#?
- How do you write the expression for the nth term of the sequence given #1, 4, 7, 10, 13,...#?
- How do you write the expression for the nth term of the sequence given #3, 7, 11, 15, 19,...#?
- How do you write the expression for the nth term of the sequence given #0, 3, 8, 15, 24,...#?
- How do you write the expression for the nth term of the sequence given #2, -4, 6, -8, 10,...#?
- How do you write the expression for the nth term of the sequence given #-2/3, 3/4, -4/5, 5/6, -6/7,...#?
- How do you write the expression for the nth term of the sequence given #2/1, 3/3, 4/5, 5/7, 6/9,...#?
- How do you write the expression for the nth term of the sequence given #1/3, 2/9, 4/27, 8/81,...#?
- How do you write the expression for the nth term of the sequence given #1, 1/4, 1/9, 1/16, 1/25,...#?
- How do you write the expression for the nth term of the sequence given #1, 2, 2^2/2, 2^3/6, 2^4/24, 2^5/120,...#?
- How do you write the expression for the nth term of the sequence given #1+1/2, 1+3/4, 1+7/8, 1+15/16, 1+31/32,...#?
- How do you write the first five terms of the sequence defined recursively #a_1=28, a_(k+1)=a_k-4#?
- How do you write the first five terms of the sequence defined recursively #a_1=15, a_(k+1)=a_k+3#?
- How do you write the first five terms of the sequence defined recursively #a_1=3, a_(k+1)=2(a_k-1)#?
- How do you write the first five terms of the sequence defined recursively #a_1=32, a_(k+1)=1/2a_k#?
- How do you write the first five terms of the sequence defined recursively #a_1=6, a_(k+1)=a_k+2#, then how do you write the nth term of the sequence as a function of n?
- How do you write the first five terms of the sequence defined recursively #a_1=25, a_(k+1)=a_k-5#, then how do you write the nth term of the sequence as a function of n?
- How do you write the first five terms of the sequence defined recursively #a_1=81, a_(k+1)=1/3a_k#, then how do you write the nth term of the sequence as a function of n?
- How do you write the first five terms of the sequence defined recursively #a_1=14, a_(k+1)=(-2)a_k#, then how do you write the nth term of the sequence as a function of n?
- Assume that #f_1,f_2,...,f_n,...# are the Fibonacci numbers. Then #AAn in NN, f_(4n)# is a multiple of #3#. Prove this statement is true?
- Sum of #n# terms of a certain series is given by #S_n=2n+3n^2#, what is the type of the series and what is its #20^(th)# term?
- How do I find the greatest lower bound for the sequence #A={\frac{1}{n+10}}_{n=1}^{\infty}#?
- #4#, #29#, #129#, #354#, #754#....?