Question

Find the 11th term of the geometric sequence of 6,-18,54...

Answer 1

In this sequence, our common ratio is -3 (each value is -3 times the previous value). The first (or 1th) term of the sequence is 6, so we can form our equation:

`y=6(-3)^(^x^-^1^)`

Now we have to find the 11 term. To do so, we plug 11 into our equation where the x would be. Once that's done, we do the math as follows:

`y=6(-3)^(^1^1^-^1^)` (plug in)

`y=6(-3)^(^1^0^)` (simplify by subtracting 1 from 11 to get 10)

`y=6(59049)` (simplify by calculating 3 to the power of 10 to get 59049)

`y=354294` (solve by multiplying 6 by 59040 to get 354294

Therefore, our 11th term in the sequence is 354394.