Scientific Notation
Find the scientific equation: 0.0023
What is 2.3 X 10-3?
number of terms
What is "n"th term?
Find S(10). 6n2 + n = Sn.
What is 610?
Given the sequence 3, 6, 12, 24, ... write an explicit formula for the sequence.
U1=3 r=2
plug into formula: Un=U1 x r(n-1)
Un=3(2)(n-1)
Find the sum of the first seven (7) terms of the geometric series
2+8+32+…
What is 10,922?
Find the standard notation of 1.4 x 102.
What is 1400?
Find the d value of: 200,140,80,20,-40,-100
What is -60?
Find the sum of the next three numbers in the sequence. 1,3,6,10,15,21,...
What is 109?
In a geometric sequence the first term is 7 and the common ratio is - 3. Find the 10th term.
U1=7 r=-3 n=10
plug into formula: Un=U1 x r^(n-1)
U10 =7(-3)^(10-1) = -137781
Find the sum of the first eight (8) terms of the geometric sequence.
–1,2,–4,…
What is 85?
Find the scientific notation of 3.002 x 105
What is 300200?
Find the d value of:3/2, 7/4, 2, 9/4, 5/2, 11/4
What is 1/4?
Find the sum of the first 64 terms of the arithmetic series: 3+9+15+21+…
What is 12,228?
Find the number of terms in the geometric sequence 1, 2, 4, 8, ..., 512.
512=1(2)^n-1
512= 2^n/2 →1024= 2^n
n=10
The first term of a geometric series is 20 and the sum to infinity is 15. What is the common ratio?
r = -1/3
Find the standard notation of 2.0 x 10-6?
What is 0.000002?
Write a formula for a1= -70 and d=-5
Un = a1 +d(n-1)
What is Un= -70 + (n-1)(-5)?
A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has only 4 cans. How many cans, in total, are in the display?
What is 108?
The second term of a geometric sequence is 6 and the fourth term is 96. Find the possible values of the first term and the common ratio.
U2=6 U4=96
U1= 3/2
r=4
Define a, r, n.
a - first term
r - ratio change
n - number of terms
Find the scientific notation of 0.0000000045.
What is 4.5 x 10-9?
Find a22 given the formula: Un=-20 + (n-1)(-4)
What is -104?
How many terms of the arithmetic sequence -3, 2, 7, ... must be added together for the sum of the series to be 116?
What is 8?
Given the sequence 4, 12, 36, 108..
Write down the next four terms of the sequence.
State what u, r, and u3 are.
Find an explicit formula for the sequence.
Verify your formula by finding the 5th & 6th terms of the sequence and comparing your answer to part a.
324, 972, 2916, 8748
u1=4 r=3 u3=36
Un=4 x (3)^ n-1
U5= 4(3)^4 U6=4(3)^5
U5=324 U6=972
Find the sum of the geometric series below.
7+21+63+…+15,309
S8=22,960
Hint: We know the values of the last term which is
an=15,309, the first term which is a1=7, and the common ratio which is r=3. Substitute these values in the formula then solve for n.
an=a1(r)^n-1
15,309 = 7(3)^n-1 15309/7 = 3^n-1
2187 = 3^n-1 3^7 = 3^n-1
7 = n-1. n=8
sn = a1(1-r^n/1-r) sn = 7(1-3^8/1-3)
sn = 7(1-6561/-2). sn = 7(-6560/-2)
sn = 7(3280) sn = 22,960