find the 8th term of the geometric sequence whose common ratio is 1/3 and whose first term is 8

Question



Answer 1

To find the 8th term of the geometric sequence, we use the formula for the n^th term of a geometric sequence:

a_n=a₁ × r^(n-1)

where:

1. a_n​ is the n-th term of the sequence.
2. a₁ is the first term of the sequence.
3. r is the common ratio of the sequence.
4. n is the term number.

The first term, the ratio, and the number of the term we need to find are all given ( a₁ ​=8 , r =1/3, n=8)

, therefore, we only need to substitute them in the formula:

a_n= a₁ × r^(n-1)

a₈= 8 × (1/3)^(8-1)

= 8 x (1/3)⁽⁷⁾

= 8 x (1 / 3⁷⁾

= 8 x (1 / 2187 )

= 8 / 2187

≈0.003659