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OpenStudy (anonymous):
What is the sum of the first 18 terms of the arithmetic series
11 + 15 + 19 + 23 + ⋯?
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OpenStudy (zzr0ck3r):
all I really used is that \(\sum_{i=1}^ni=\frac{n(n+1)}{2}\)
OpenStudy (anonymous):
is it 810
?
OpenStudy (zzr0ck3r):
\(\sum_{n=1}^{18}7+4n=\sum_{n=1}^{18}7+4\sum_{n=1}^{18}n=18*7+4(\frac{18*19}{2})=810\)
OpenStudy (zzr0ck3r):
yes:)
OpenStudy (anonymous):
thanks
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OpenStudy (zzr0ck3r):
how did you do it, so I know how to explain it to others without the notation and method I used.
OpenStudy (anonymous):
i did it the hard way just adding 4 to every number and just add until you reach the 18th term
OpenStudy (zzr0ck3r):
oh well notice with my way you can now do the 1200000th term
OpenStudy (zzr0ck3r):
just change where you see an 18 to 1200000
OpenStudy (anonymous):
yeah and thanks
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OpenStudy (zzr0ck3r):
ok good luck, if you ask another someone else might have an easier way. I know there is, but I never studied arithmetic sequences....
hartnn (hartnn):
there is a simple formula for sum of terms in an arithmetic sequences.
you just need 1st term, common difference and number of terms
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