The second term of a geometric sequence is and the sixth term is 2 and 32 The first term, a and the common ratio, r.

There are two sets of solutions:

Step-by-step explanation:

The question states that and should represent the first term and the common ratio of this geometric sequence, respectively. Therefore:

Let denote a positive whole number. In general, the -th term of this geometric sequence would be .

The sixth term of this sequence would thus be .

The fact that the second term is and the sixth term is gives two equations about and :

.

Take the quotient of these two equations to eliminate :

.

.

There are two possible roots: either or .

When , substitute back to the first equation and solve for : .

On the other hand, when , substituting back and solving for would give .

Substitute these values into the second equation. Either set of values will work.

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