SOLUTION: 1,2,0.5,5,0.25,8..... Calculate the sum of 100 terms of the sequence

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Question 738254: 1,2,0.5,5,0.25,8..... Calculate the sum of 100 terms of the sequence
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
1,2,0.5,5,0.25,8..... 

Change the decimals to fractions:

1,  2, 1%2F2, 5, 1%2F4, 8, ...

the odd numbered terms are 50 terms of this geometric sequence

1, 1%2F2, 1%2F4, ...

We use the formula 

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

where n=50, a1 = 1, r = 1%2F2

S50 = 1%281-%281%2F2%29%5E50%29%2F%281-1%2F2%29 

Since %281%2F2%29%5E50 is so small it is negligible and

that is essentially 1%2F%281%2F2%29 = 2

the even numbered terms are 50 terms of this arithmetic sequence

2,5,8,...

We use the formula

Sn = n%2F2[2a1 + (n-1)d]

S50 = 50%2F2[2·2 + (50-1)3]

S50 = 25[4 + 49·3]

S50 = 3775

Answer:  2 + 3775 = 3777. 

Edwin