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anonymous
 one year ago
Find S11 for 3 + 1 + (1) + (3) +…
A. 77
B. 75
C. 73
D. 71
anonymous
 one year ago
Find S11 for 3 + 1 + (1) + (3) +… A. 77 B. 75 C. 73 D. 71

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jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.0hmm doesn't look like a sequence to me for one

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.0can you post a quick screenshot of the material? so we can see what you mean

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Nope, it's a series

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So we can use sum of an arithmetic series equation I guess which is \[S_n = \frac{ n }{ 2 }[2a+(na)d]\] a = first term in series, d = common difference

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3n is what you're looking for in this case n = 11

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So what's the common difference, look at your previous post what I wrote when you left

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So I'll post it again for reference, the common difference is \[t_2t_1=t_3t_2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm really confused right now..

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3I would say so you jumped from a sequence from your last question to a series here, so just focus on the equation for now. The t here represents the term and the subscript is the address of the term, so \[t_1 = 3~~~t_2 = 1\] etc

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0Common difference can be worked out by subtracting the first term from the second

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3\[t_2t_1 = t_3t_2 \implies 13 = 11 \implies 2 = 2 \checkmark\] so it works out, our common difference d = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i'm just writing everything down in my notebook!

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Ok cool :) Well now lets find a, what is a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is already one of the terms given, or do I have to find it?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3a = first term in series

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So we now have d = 2, a = 3, n = 11

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Now we can use the equation I mentioned above \[S_n = \frac{ n }{ 2 }[2a+(na)d]\] can you plug it all in now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sn=11/2 (2(3)+(11+3)2) correct?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Close, your sign in (na) is off but it looks good \[S_{11} = \frac{ 11 }{ 2 }[2(3)+(113)(2)]\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Yup, that looks good

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but it isn't one of the choices?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So is your question asking for \[S_{11}\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So it's exactly Find S11 for 3 + 1 + (1) + (3) +… right

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Mhm, everything looks right

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Ok lets see...a = 3, d = 2, n = 11

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3I have located the problem it's the original equation I gave you, it should (n1) not (na) sorry! \[S_n = \frac{ n }{ 2 }[2a+(n1)d] = \frac{ 11 }{ 2 }[2(3)+(111)(2)] = \]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3So the equation is \[S_n = \frac{ n }{ 2 }[2a+(n\color{red}1)d]\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Nope, you must've put in wrong

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ 11 }{ 2 }[2(3)+(111)(2)] = \frac{ 11 }{ 2 }[6+10(2)] = \frac{ 11 }{ 2 }[620]=\frac{ 11 }{ 2 }(14) = 77\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Use your order of operations :)
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