Answer:
the 7th term of the geometric sequence with common ratio 1/3 and first term 7 is 7/729.
Explanation:
The general formula for the nth term of a geometric sequence with first term a and common ratio r is:
an = ar^(n-1)
In this problem, the first term a is 7 and the common ratio r is 1/3. Substituting these values into the formula, we get:
a7 = 7(1/3)^(7-1)
Simplifying the exponent, we get:
a7 = 7(1/3)^6
To evaluate this expression, we can first simplify the denominator by using the fact that (1/3)^2 = 1/9:
(1/3)^6 = (1/3)^2 * (1/3)^2 * (1/3)^2 = (1/9)^3 = 1/729
Substituting this value back into the equation, we get:
a7 = 7(1/729)
Simplifying this expression, we get:
a7 = 7/729
Therefore, the 7th term of the geometric sequence with common ratio 1/3 and first term 7 is 7/729.