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Mathematics 38 Online
OpenStudy (anonymous):

show that the series 5+6+7+........+105 has 101 terms.

OpenStudy (ash2326):

@Hollywood_chrissy this is an arithmetic sequence with first term =5. last term or nth term =105 and common difference= (6-5)=1 so Can you do it now?

OpenStudy (anonymous):

so you subtract 5 from all the terms?

OpenStudy (ash2326):

no, we don't need to do that

OpenStudy (ash2326):

@Hollywood_chrissy have you studied arithmetic sequences?

OpenStudy (anonymous):

how many terms are there from 1 to 105 ?

OpenStudy (anonymous):

104

OpenStudy (ash2326):

@Hollywood_chrissy how many terms are these? 1, 2, 3, 4???

OpenStudy (anonymous):

4

OpenStudy (anonymous):

well.. 1 to 105 are 105 terms,,as 1 to 3 are 3 terms ,,and not 2..are you getting me/

OpenStudy (ash2326):

that;s (4-1 ) =>3 +1

OpenStudy (ash2326):

I meant, just subtract the first term from the last term and add 1. This will only work, when the terms have a difference of 1 like here. @Hollywood_chrissy can you tell the no. of terms?

OpenStudy (anonymous):

a=5, d=1 and n=101 now use formula sn=n/2{2a+(n-1)d

OpenStudy (anonymous):

now put values in formula.

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