1. Find the 7th term of 6, 18, 54, ...
2. Find the 11th term of 3, 6, 12, ...
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1. Find the 7th term of 6, 18, 54, ...
2. Find the 11th term of 3, 6, 12, ...
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Answer:
1458
Explanation:
How do we get from
2
to
6
? One way is to multiply by
3
.
How do we get from
6
to
18
? We can multiply by
3
once again.
What about
18
to
54
? Again, we can multiply by
3
.
We notice that our common ratio is
3
. We can leverage this fact to write the next terms of our sequence:
...
54
,
(
54
⋅
3
)
,
(
54
⋅
3
2
)
,
(
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
=
1458
Hope this helps!