56.5K Shares
twitter facebook tumblr reddit quora medium
Share to Quora
Successfully copied the web link. You cloud share these fun content to quora!
Find $a_{1}$ if $a_{8}=54$ and $a_{9}=60$.

Find $a_{1}$ if $a_{8}=54$ and $a_{9}=60$.

Actualizado en

Question

Find a1a_(1) if a8=54a_(8)=54 and a9=60a_(9)=60.

Best Answer

We don’t have enough information to find the common difference dd, so we can’t use the formula an=a1+(n1)da_(n)=a_(1)+(n-1)d directly. However, notice that a9=a8+da_(9)=a_(8)+d, so d=a9a8=6054=6d=a_(9)-a_(8)=60-54=6.
Now we can use the formula an=a1+(n1)da_(n)=a_(1)+(n-1)d. Plugging in a8=54a_(8)=54, we have:
54=a1+(81)(6)54=a_(1)+(8-1)(6)
Simplifying:
54=a1+4254=a_(1)+42
Subtracting 42 from both sides:
a1=12a_(1)=12
Therefore, a1=12a_(1)=12.