Question

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?

Answer 1

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