The third term in a geometric sequence is - 81. The common ratio is 1/3

What is the second term of the sequence?

If you answer, can you explain it?

Step-by-step explanation:

The formula for the nth term of a geometric sequence is expressed as follows

Tn = ar^ (n - 1)

Where

Tn represents the value of the nth term of the sequence

a represents the first term of the sequence.

n represents the number of terms.

From the information given,

r = 1/3

T3 = - 81

n = 3

Therefore,

- 81 = a * 1/3^ (3 - 1)

-81 = a * (1/3) ^2

-81 = a/9

a = - 81 * 9 = - 729

The exponential equation for this sequence is written as

Tn = - 729 * (1/3) ^ (n-1)

Therefore, to find the second term, T2, n = 2. It becomes

T2 = - 729 * (1/3) ^ (2-1)

T2 = - 729 * (1/3) ^1

T2 = - 729 * (1/3)

T2 = - 243