3. Write the given several sequences below. Say what the next two terms would be in the sequence.

Key takeaway: These are patterns written in powers of 3. The main task is to look at how the exponents change from term to term.

a. $3, 3^2, 3^3, \ldots$

The exponents increase by $1$ each time:

$3^1, 3^2, 3^3, \dots$

So the next two terms are:

$3^4,\ 3^5$

b. $3, 3^4, 3^7, \ldots$

The exponents increase by $3$ each time:

$3^1, 3^4, 3^7, \dots$

So the next two terms are:

$3^{10},\ 3^{13}$

c. $3, 3^7, 3^{10}, \ldots$

Here the exponents shown are $1, 7, 10$. From $7$ onward, the pattern increases by $3$:

$3^7, 3^{10}, 3^{13}, 3^{16}, \dots$

So the next two terms are:

$3^{13},\ 3^{16}$

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Pitfalls the pros know 👇 Do not change the base from $3$ to something else, and do not look only at the visible numbers outside the exponents. The pattern is in the exponent sequence, not in the decimal value of the terms.

What if the problem changes? If your teacher intended the exponent pattern in part (c) to start from $1$ and then follow a different rule, the next terms would change. The safe method is always to identify the exponent pattern directly from the list given.

Tags: exponent pattern, sequence terms, power of 3