we know that a₁ = 1, and aₙ = aₙ₋₁ + 2, is another way of saying, we add 2 to get the next term, namely, 2 is the common difference.
![\bf n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=1\\ d=2\\ n=7 \end{cases} \\\\\\ a_7=1+(7-1)2\implies a_7=1+12\implies a_7=13](https://tex.z-dn.net/?f=%5Cbf%20n%5E%7Bth%7D%5Ctextit%7B%20term%20of%20an%20arithmetic%20sequence%7D%0A%5C%5C%5C%5C%0Aa_n%3Da_1%2B%28n-1%29d%5Cqquad%0A%5Cbegin%7Bcases%7D%0An%3Dn%5E%7Bth%7D%5C%20term%5C%5C%0Aa_1%3D%5Ctextit%7Bfirst%20term%27s%20value%7D%5C%5C%0Ad%3D%5Ctextit%7Bcommon%20difference%7D%5C%5C%5B-0.5em%5D%0A%5Chrulefill%5C%5C%0Aa_1%3D1%5C%5C%0Ad%3D2%5C%5C%0An%3D7%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0Aa_7%3D1%2B%287-1%292%5Cimplies%20a_7%3D1%2B12%5Cimplies%20a_7%3D13)
The value of Mr Banks's property was $250,000
What percentage of the property is left for charity?
The percentage of property left for charity can be determined as the 100% of the property minus all percentages given to others
% left for charity=100%-50%-22%-16%
% left for charity=12.00%
12.00% of the property=$30,000
1.00% of the property =$30,000/12
1.00% of the property =$2,500
100.00% of the property=$2500*100
100.00% of the property=$250,000
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I find these easier to calculate when everything is converted to a decimal
d=rt
d=(9.5mph x 1.75)
d = 16.625 ( approx. 16.6 miles)
Answer:
Happy paws
y = 20 + 4x
Woof watchers
y = 9 + 5x
x = 11 hours
Step-by-step explanation:
Let
Number of hours = x
Total cost = y
Total cost = fixed cost + variable cost
The equations are:
Happy paws
y = 20 + 4x
Woof watchers
y = 9 + 5x
solve the equation to find for how many hours the total cost of the services is equal.
Equate total cost of both services
20 + 4x = 9 + 5x
Collect like terms
20 - 9 = 5x - 4x
11 = x
x = 11 hours
Check:
Happy paws
y = 20 + 4x
= 20 + 4(11)
= 20 + 44
= 64
Woof watchers
y = 9 + 5x
= 9 + 5(11)
= 9 + 55
= 64
