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)   (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, , 5, , 8, ...

the odd numbered terms are 50 terms of this geometric sequence

1, , , ...

We use the formula 

Sn =  

where n=50, a1 = 1, r = 

S50 =  

Since  is so small it is negligible and

that is essentially  = 2

the even numbered terms are 50 terms of this arithmetic sequence

2,5,8,...

We use the formula

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

S50 = [2·2 + (50-1)3]

S50 = 25[4 + 49·3]

S50 = 3775

Answer:  2 + 3775 = 3777. 

Edwin
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