SOLUTION: How many terms of the series 2 + 2√2 + 4 .....will amount to 30 + 14√2

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Question 788794: How many terms of the series 2 + 2√2 + 4 .....will amount to 30 + 14√2
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

2 + 2√2 + 4

That's a geometric series with common ratio r = √2 

Geometric sequence:

Sn = a%5B1%5D%281-r%5En%29%2F%281-r%29

Sn = a%5B1%5D%281-r%5En%29%2F%281-r%29 

30 + 14√2 = 2%281-%28sqrt%282%29%29%5En%29%2F%281-sqrt%282%29%29

(30 + 14√2)(1 - √2) = 2·[1 - (√2)n

30 - 16√2 - 14·2 = 2 - 2(√2)n

Divide every term by 2

15 - 8√2 - 14 = 1 - (√2)n

1 - 8√2 = 1 - (√2)n

-8√2 = -(√2)n

8√2 = (√2)n

Write 8 as 23 and √2 as 2.5

232.5 = (2.5)n

23.5 = 2.5n

Equate the powers of 2

3.5 = .5n

3.5%2F.5 = n

7 = n

Answer: It will take 7 terms for the sum to amount to 30 + 14√2   
Edwin