
Finding Nth Term
Dear Forum , I have to Find the nth term of the geometric sequence for the following,
8,4/3,2/9...
I was curious if my following work is correct , please let me know what you think:
8,(4)/(3),(2)/(9)
Remove all extra parentheses from the expression.
8,(4)/(3),(2)/(9)
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by (1)/(6) gives the next term. In other words, an=r*an1.
Geometric Sequence: r=(1)/(6)
This is the form of a geometric sequence.
an=a1r^(n1)
Substitute in the values of a1=8 and r=(1)/(6).
an=8*(1)/(6^(n1))
Multiply 8 by (1)/(6^(n1)) to get (8)/(6^(n1)).
an=(8)/(6^(n1))
Substitute in the value of n to find the nth term.
a2=(8)/(6^((2)1))
Remove the parentheses around the expression 2.
a2=(8)/(6^(21))
Subtract 1 from 2 to get 1.
a2=(8)/(6)
Reduce the expression (8)/(6) by removing a factor of 2 from the numerator and denominator.
a2=(4)/(3)

That is the correct basic idea. But you forgot the signs.
$\displaystyle 8\left(\frac{{\color{red}}1}{6}\right)^{n1}$