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!! :))

cosign Feb 1, 2022

#1**+2 **

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!

BuilderBoi Feb 1, 2022

#3**+2 **

\(18\) 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