What is the 7th term of this geometric sequence 2, 6, 18, 54, …?

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Answer 1 · 2018-06-24T01:36:56

$1458$ $1458$

How do we get from $2$ $2$ to $6$ $6$ ? One way is to multiply by $3$ $3$ .

How do we get from $6$ $6$ to $18$ $18$ ? We can multiply by $3$ $3$ once again.

What about $18$ $18$ to $54$ $54$ ? Again, we can multiply by $3$ $3$ .

We notice that our common ratio is $3$ $3$ . We can leverage this fact to write the next terms of our sequence:

$...54, (54*3), (54*3^2), color(blue)((54*3^3))$

Notice, we are multiplying by three every time. The $7$ th term of this sequence is given by the blue expression

$54*3^3$ , which is equal to

$54*27=color(blue)(1458)$

Hope this helps!