Question
Determine the 5th term in the sequence defined by gn = 9 ⋅ (1/3 )n − 1
Answers
GPT 3.5
To find the 5th term in the sequence, we need to substitute n=5 into the formula for the nth term.
g₅ = 9 ⋅ (1/3 )^(5-1)
Simplifying the exponent:
g₅ = 9 ⋅ (1/3)^4
Since 1/3 raised to the power of 4 is (1/3)^4=1/(3^4)=1/81, we can substitute this value into the equation:
g₅ = 9 * (1/81)
Multiplying numerator and denominator by 9:
g₅ = 9/81
Simplifying the fraction:
g₅ = 1/9
Therefore, the 5th term in the sequence is 1/9.
g₅ = 9 ⋅ (1/3 )^(5-1)
Simplifying the exponent:
g₅ = 9 ⋅ (1/3)^4
Since 1/3 raised to the power of 4 is (1/3)^4=1/(3^4)=1/81, we can substitute this value into the equation:
g₅ = 9 * (1/81)
Multiplying numerator and denominator by 9:
g₅ = 9/81
Simplifying the fraction:
g₅ = 1/9
Therefore, the 5th term in the sequence is 1/9.