Question

The first term of a geometric sequence is -2 and the common ratio is 3 what is the 12th term of the sequence

Answer 1

The 12th term of a geometric sequence with a first term of -2 and a common ratio of 3 is calculated using the formula for the nth term, resulting in -354294.

Step-by-step explanation:

To find the 12th term of a geometric sequence, we use the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number. Given that the first term a1 is -2 and the common ratio r is 3, we can calculate the 12th term:

a12 = -2 × 3(12-1)

a12 = -2 × 311

a12 = -2 × 177147

a12 = -354294

The 12th term of the sequence is -354294.

Answer 2

The n-th term of a geometric sequence with initial value a and common ratio r is given by
`a_n=a_1r^(n-1)`.

We have
`a_1=-2` and
`r=3` and
`n=12`

Substitute:

`a_(12)=-2\cdot3^(12-1)=-2\cdot3^(11)=-2\cdot177147=-354294`