Final answer:
To find the 9th term in the geometric sequence with the first term 1 and common ratio -1/3, we use the formula an = a1 × r^(n-1). Substituting n with 9, we get the 9th term as 1 × (-1/3)^8, which simplifies to 1/6561.
Step-by-step explanation:
To find the 9th term in a geometric sequence given the first term (a1) is 1 and the common ratio (r) is -1/3, we use the formula for the nth term of a geometric sequence, which is an = a1 × rn-1. For the 9th term, we substitute n with 9:
a9 = 1 × (-1/3)9-1
= 1 × (-1/3)8.
Since (-1/3)8 is a positive number (because the base is negative and the exponent is even), and 1/3 raised to the 8th power is a small positive fraction, we calculate:
a9 = 1 × (1/6561).
Therefore, the 9th term of the sequence is 1/6561.