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The average of a sequence of n numbers is 10. If the numbers 20 and 30 are added to this sequence to form a sequence of n + 2 terms, the average of the sequence increases to 12. What is the value of n?

 

So I tried adding the two numbers 20 + 30 which increased the average by 2 which I can try to make an equation but I am having trouble continuing 

Any ideas?

 

appreciate the help!! :))

 Feb 1, 2022
 #1
avatar+2444 
0

For the original sequence: \({\text {sum}\over n } = 10\)

 

When you add the terms \(20\) and \(30\), we have the equation: \({{\text{sum} + 50}\over{n+2}} = 12\)

 

These two are a equations form a system, and you can solve for \(n\) from here.

 

Good Luck!

 Feb 1, 2022
 #2
avatar+83 
+1

Thank you I got it from here!

 

I got

 

sum = 10n

soo

 

(10n+50)/(n+2)=12

cross multiplying we get

 

10n+50 = 12n+24

therefore we get n= 18

cosign  Feb 1, 2022
edited by cosign  Feb 1, 2022
 #3
avatar+2444 
+1

\(18\) is incorrect. Here is how you solve it:

 

\({\text {sum}\over n} = 10\)

\(\text {sum} = 10n\)

\({{10n+50}\over {n+2}} = 12\)

\({10n+50} = 12n+24\)

\(50 = 2n+24\)

\(26 = 2n\)

\(n=13\)

 

Thus, there are \(\color{brown}\boxed{13}\) terms in the original sequence that make for a mean of \(10\), and when the numbers \(20\) and \(30\) are added, the sum becomes \(180\), making the mean \(12\).

BuilderBoi  Feb 2, 2022

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