Question

What is the explicit rule for the nth term of the sequence:

a) an =3 × (−2) n−1

b) an =3 × (− 2)n−1

c) an = 3 × ( 2)n−1

d) an = 3 × ( 2)n−1

Answer 1

The question refers to the explicit rule for the nth term of a sequence and highlights the importance of the base and the position of the negative sign in exponentiation, which affects the value of the nth term.

Step-by-step explanation:

The student is asking about the explicit rule for the nth term of a sequence. It is important to note the distinction in the options provided. For options (a) and (b), we have negative bases raised to the nth power, whereas options (c) and (d) have positive bases. The explicit rule describes a formula that allows you to find the nth term of a sequence without listing all the preceding terms. In these options, an represents the nth term, 3 is a constant multiplier, and the base raised to the power of n-1 varies as either -2 or 2. Issues like whether there is a space between the base and the exponent, or whether the negative sign is inside or outside the exponentiation, are critical since they change the sequence values significantly.