Final answer:
The nth term of the sequence is given by the formula 4 × (-2)^{n-1}. The seventh term a7 is 256.
Step-by-step explanation:
To find the rule for the nth term of the sequence 4,-8,16,-32, we observe that each term is obtained by multiplying the preceding term by -2.
Thus, starting with the first term as 4 (or 2^2), the nth term, an, can be expressed as 4 × (-2)n-1. To find the seventh term of the sequence, a7, we substitute n with 7 in our formula:
a7 = 4 × (-2)7-1 = 4 × (-2)6 = 4 × 64 = 256