Step 1:

Consider the arithmetic sequence is .

Find the common difference.

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.

The common difference is .

Add to the third term to find the fourth term, and so on.

.

.

.

The first six terms of the sequence are .

Step 2:

Find the explicit formula for term.

Formula for term of arithmetic sequence is .

Substitute and in term of arithmetic sequence.

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Step 3:

The explicit formula .

The term:

Substitute in .

.

The term is .

Solution:

(a) The first six terms of the sequence are .

(b) The common difference is ;.

(c) The term is .

Step 1:

Consider the geometric sequence is .

Find the common ratio .

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The common ratio is .

Multiply with to the third term to find the fourth term and so on.

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The first four terms of the sequence are .

Find the explicit formula for term.

Formula for term of geometric sequence is .

Substitute and in term of geometric sequence.

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The explicit formula .

Step 3:

Find the sixth term.

Substitute in .

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The sixth term is .

Solution:

(a) The first six terms of the sequence are .

(b) The common difference is ;.

(c) The term is .