+91 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!! :))
+2666 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!
+2666 \(18\) 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 \(12\).
