A geometric sequence is represented by an = a1rn-1. What is the 7th term of a geometric sequence in which a1 = - 243 and the common ratio is - 1/3?

-1/3

-1/9

1/9

1/3

Answer: the 7th term of the geometric sequence is 1/3

Step-by-step explanation:

The formula for determining the nth term of a geometric progression is expressed as

an = a1r^ (n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a1 = - 243

r = - 1/3

n = 7

The 7th term, a7 is

a7 = - 243 * - 1/3^ (7 - 1)

a7 = - 243 * - 1/3^6

a7 = - 3^5 * - 3^6

a7 = 3^ (5 - 6)

a7 = 3^ - 1

a7 = 1/3