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