## 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. 6*x*

B. 10.5*x*

C. 11*x*

D. 12*x*

E. 32*x*

## 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 2*x* because the previous term is simply multiplied by 2. When you get to the third term, 2(2*x*) can be simplified to 4*x*. This pattern continues:

Terms: *x*, 2*x*, 4*x*, 8*x*, 16*x* , 32*x*

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

*x* + 2*x* + 4*x* + 8*x* + 16*x* + 32*x* = 63* **x*

63*x* divided by 6 is 10.5*x*

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

The correct answer is (B).

This is a medium level question.

**Want some help reviewing the math concepts you need to master? **Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.