Question

Write a rule for a geometric sequence that has -6 as its first term and a common ratio of 2. What is the tenth term of this sequence?

A) A(n) = 2 * -6^10-1; -20,155,392
B) A(n) = -6 * 2^n; -6144
C) A(n) = -6 * 2^n-1; -3072
I need this Answered ASAP, Thank you

Answer 1

The general form of the geometric sequence is
`a_(n) = a_(1) (r) ^(n-1)`, where a sub n is the number term you're looking for (we're looking for the tenth term). a sub 1 is the first term in the sequence (ours is -6), r is the common ratio, and n-1 is the numbered term you're looking for minus 1. Our formula then looks like this:
`a_(10) =-6(2) ^(10-1)`. Simplify it to
`a_(10) =-6(2)^9`. Take 2 to the 9th power then multiply it by -6 to get -3072. C is your answer.