Kevin F. answered • 12/17/13

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word problems and turning them into algebraic equation to slove

Find the

3,6,12,24,48,96,.............

Find the

**sum**of the first 10 terms of the following sequence by using a formula. which one should you use?3,6,12,24,48,96,.............

First notice that the terms show a pattern:

3 = 3 x 1 = 3 x 2

^{0} 6 = 3 x 2 = 3 x 2

^{1}12 = 3 x 4 = 3 x 2

^{2}24 = 3 x 8 = 3 x 2

^{3}48 = 3 x 16 = 3 x 2

^{4}96 = 3 x 32 = 3 x 2

^{5}Each number in the sequence is double the previous number. Therefore, the next four terms are 192, 384, 768, 1536.

The terms and the running sum looks like this:

num sum

----- -----

3

6 - 9 = 3 x 3

12 - 21 = 3 x 7

24 - 45 = 3 x 15

48 - 93 = 3 x 31

96 - 189 = 3 x 63

...

Thus the pattern, or formula for the sum of the 1st through nth terms is:

3 * (2

^{n }- 1)And the sum of the first 10 terms is:

3 * (2

^{10}- 1)= 3 * (1024 - 1)

= 3 * 1023

= 3069