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Find the sum of series 5+7+9+10+13+13+17+16+....., upto 40 terms?

Please help i am facing problem while solving this question.i have tried my best to solve this but unable to find the common difference.?

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closed as off-topic by Sjoerd C. de Vries, Daniel Lichtblau, Michael E2, Verbeia Nov 23 '13 at 21:27

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2  
The terms in your sum are not an arithmetic progression. You could use FindSequenceFunction to come up with a general formula, which might or might not be correct. –  Michael E2 Nov 23 '13 at 16:14
    
is 5+7+9+10+13+13+17+16+... defined by =(5)+(7)+(5+4)+(7+3)+(5+4+4)+(7+3+3)+(5+4+4+4)+(7+3+3+3)+...+(5+n*4)+(7+n*3) ? In that case it is (5+7)+(9+10)+(13+13)+(17+16)... , ie 12+19+26+33+... which is a arithmetic progression –  andre Nov 23 '13 at 17:02
    
Do you realize that there are infinitely many series that begin as yours does? –  David Carraher Nov 23 '13 at 18:50
2  
This question appears to be off-topic because it is about math homework, not Mathematica. –  Daniel Lichtblau Nov 23 '13 at 21:15

1 Answer 1

This provides a nice application for FindSequenceFunction, as suggested by Michael

f = FindSequenceFunction[{5, 7, 9, 10, 13, 13, 17, 16}]
1/4 (14 + 2 (-1)^#1 + 7 #1 - (-1)^#1 #1) &

You can check that this sequence f starts out as specified:

f /@ Range[10]
{5, 7, 9, 10, 13, 13, 17, 16, 21, 19}

To calculate the sum of the first 40 terms:

Total[f /@ Range[40]]
1570
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