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SAT Math: Arithmetic

Sequences

If the first term in a sequence is x and each term after the first is 2 times the term before it, what is the average of the first 6 terms of the sequence in terms of x?

A.   6x

B.   10.5x

C.  11x

D.   12x

E.  32x

 

Knowsys Method

Read the question carefully.  You need to make sure that you recognize the pattern.

Identify the bottom line.  Find the average of the first six terms.

Assess your options.  You cannot work backwards from the answer in this problem without a lot of confusing steps, so start with the information that you have been given and determine the terms in the sequence.

 Attack the problem.  The first term is x.  The second term will be 2x because the previous term is simply multiplied by 2.  When you get to the third term, 2(2x) can be simplified to 4x.  This pattern continues:  

Terms: x, 2x, 4x, 8x, 16x , 32x

Now use the average formula.  Take the sum of the numbers and divide it by 5. 

x + 2x + 4x + 8x + 16x  + 32x = 63 x

63x divided by 6 is 10.5x

Loop back.  You solved for your bottom line!  Select your answer.

 

The correct answer is (B). 

This is a medium level question.

 

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