A. Sigma notation
The formula for finding the nth value of the geometric series
is given as:
an = a1 * r^n
Where,
an = nth value of the series
<span>a1 = 1st value in the geometric series = 940</span>
r = common ratio = 1/5
n = nth order
The sigma notation for the sum of this infinite geometric
series is therefore,
(see attached photo)
B. Sum of the infinite geometric series
The formula for calculating the sum of an infinite
geometric series is given as:
<span>S = a1 / (1 – r)</span>
Substituting the given values:
S = 940 / (1 – 1/5)
<span>S = 1,175</span>
Lisa has 21 books because you add 1 to Felix because she Lisa had 1 more than him & Joe has 10 than Lisa .
1/5(3x - 0.5) + 1/6= x/5 + 0.5
change decimals to fractions (0.5=1/2)
1/5(3x - 1/2) + 1/6= x/5 + 1/2
multiply 1/5 by each term in parentheses
(1/5*3x) + (1/5*-1/2) + 1/6= x/5 + 1/2
multiply within parentheses
3x/5 - 1/10 + 1/6= x/5 + 1/2
need a common denominator; all denominators go into 30
18x/30 - 3/30 + 5/30= 6x/30 + 15/30
combine like terms
18x/30 + 2/30= 6x/30 + 15/30
subtract 6x/30 from both sides
12x/30 + 2/30= 15/30
subtract 2/30 from both sides
12x/30= 13/30
multiply both sides by 30 to eliminate fractions
(12x/30)(30)= (13/30)(30)
12x= 13
divide both sides by 12
x= 13/12 or 1.083333
ANSWER: x= 13/12 or 1.083333
Hope this helps! :)
Answer:
52.8
Step-by-step explanation:
Lets Sean's age be x
Helen's age by y
x/y=3/5
x=3/5y
Second equation
2(x-2)=y-2
on solving u get Helen as 10 and Sean as 6
