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Write the explicit formula for the sequence below and use it to find the 16th term:

6, -24, 96, -384, . . .

User Sam Claus
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1 Answer

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Given:

The sequence is:


6, -24, 96, -384,...

To find:

The explicit formula for the given sequence and then find the 16th term.

Solution:

We have,


6, -24, 96, -384,...

The ratio between two consecutive terms are:


(-24)/(6)=-4


(96)/(-24)=-4


(-384)/(96)=-4

The given sequence has a common ratio. So, the given sequence is a geometric sequence with first term 6 and common ratio
-4.

The explicit formula of a geometric sequence is:


a_n=ar^(n-1)

Where, a is the first term and r is the common ratio.

Putting
a=6, r=-4 in the above formula, we get


a_n=6(-4)^(n-1)

We need to find the 16th term. So, put
n=16 in the above formula.


a_n=6(-4)^(16-1)


a_n=6(-4)^(15)


a_n=6(-1073741824)


a_n=-6442450944

Therefore, the explicit formula for the given sequence is
a_n=6(-4)^(n-1) and 16th term of the given sequence is

-6.442450944.

User Richard Poirier
by
7.8k points

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