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
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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
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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 = = = =
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Adding the two sums together
610 + 2097150 = 2097760
Edwin
