
Kevin F. answered 12/17/13
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word problems and turning them into algebraic equation to slove
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,.............
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 20
6 = 3 x 2 = 3 x 21
12 = 3 x 4 = 3 x 22
24 = 3 x 8 = 3 x 23
48 = 3 x 16 = 3 x 24
96 = 3 x 32 = 3 x 25
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 * (2n - 1)
And the sum of the first 10 terms is:
3 * (210 - 1)
= 3 * (1024 - 1)
= 3 * 1023
= 3069