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Mathematics 16 Online
OpenStudy (anonymous):

What is the sum of the first 18 terms of the arithmetic series 11 + 15 + 19 + 23 + ⋯?

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

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

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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