SOLUTION: Determine the sum of the first 40 terms of the following series: 2+2+5+4+8+8+11+16+...

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Question 841929: Determine the sum of the first 40 terms of the following series:
2+2+5+4+8+8+11+16+...

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
                             2+2+5+4+8+8+11+16+...

The odd-numbered terms are   2 + 5 + 8 + 11  + ... 
The even-numbered terms are    2 + 4 + 8  + 16 +...

The first 40 terms are 20 terms of each of those sequences

---------------------------------------------

The first sequence is:

2 + 5 + 8 + 11  + ... 

which is an arithmetic sequence with a1=2, d=3, n=20

so we use this sum formula 

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

S20 = [2(2) + (20-1)3] = 10[4 + (19)3] = 10[4+57] = 10[61] = 610

-------------------------------------

The second sequence

2 + 4 + 8  + 16 +...

which is an geometric sequence with a1=2, r=2, n=20

so we use this sum formula 

Sn = 

S20 =  =  =  = 

------------------------------------

Adding the two sums together

610 + 2097150 = 2097760  
 
Edwin
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