Is 7/11 and 42/60 proportional?
1 answer:
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The pattern is formed a geometric sequence
The nth term of the sequence is
Step-by-step explanation:
The formula of the nth term of a geometric sequence is:
, where
- a is the first term
- r is the common ratio between the consecutive terms
∵ The pattern is 3 , 9 , 27 , 81 , 243
∵ 9 ÷ 3 = 3
∵ 27 ÷ 9 = 3
∵ 81 ÷ 27 = 3
∵ 243 ÷ 81 = 3
- There is a common ratio 3 between each two consecutive terms
∴ The pattern is formed a geometric sequence
∵ The first term is 3
∴ a = 3
∵ The common ratio is 3
∴ r = 3
- To find the nth term substitute a and r in the formula above
∵
∴
- Remember we add the powers of the same base with multiplication
∵ 3 × =
∴ 3 × =
∴
∴ The nth term of the sequence is
Learn more:
You can learn more about the sequences in brainly.com/question/1522572
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The solution is price of 1 slice of pizza is $ 1.75 and price of 1 bottle of water is $ 1.25
<em><u>Solution:</u></em>
Let "p" be the price of 1 slice of pizza
Let "b" be the price of 1 bottle of water
<em><u>Given that Abby bought two slices of pizza and three bottles of water for $7.25</u></em>
So we can frame a equation as:
two slices of pizza x price of 1 slice of pizza + three bottles of water x price of 1 bottle of water = $ 7.25
2p + 3b = 7.25 ------- eqn 1
<em><u>Cameron bought four slices of pizza and one bottle of water for $8.25</u></em>
So we can frame a equation as:
four slices of pizza x price of 1 slice of pizza + one bottles of water x price of 1 bottle of water = $ 8.25
4p + 1b = 8.25 ----- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "p" and "b"</u></em>
Multiply eqn 1 by 2
4p + 6b = 14.5 ----- eqn 3
Subtract eqn 2 from eqn 3
4p + 6b = 14.5
4p + 1b = 8.25
( - ) ------------------
5b = 6.25
<h3>b = 1.25</h3>Substitute b = 1.25 in eqn 1
2p + 3b = 7.25
2p + 3(1.25) = 7.25
2p + 3.75 = 7.25
2p = 3.5
<h3>p = 1.75</h3><em><u>Thus the solution is:</u></em>
price of 1 slice of pizza = $ 1.75
price of 1 bottle of water = $ 1.25