Question

What is the sum of the geometric sequence 3,12,48... if there are 8 terms?

Answer 1

Answer:

  C)  65,535

Step-by-step explanation:

You can add up the 8 terms ...

  3, 12, 48, 192, 768, 3072, 12288, 49152

to find their sum is 65535.

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Estimating

Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.

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Using the formula

You know the formula for the sum of a geometric sequence is ...

  S = a1(r^n -1)/(r -1)

where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).

Filling in the values, you find the sum is ...

  S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535