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How to get the formula for Sn of an arithmetic series?

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Tn = a+(n -1)d

sn = n/2(a + n)

4. For the series 3 + 9 + 15 + 21... Find:
a) an expression for tn
b) an expression for sn
c) the answer if s = 20
d) the answer if t = 115

5. Find the # of terms in the sequencece 2,6,10... 626

I need a step by step procedure for solving these problems.

https://brainmass.com/math/algebra/get-formula-arithmetic-series-5082

SOLUTION This solution is FREE courtesy of BrainMass!

4. In this series a=3, d=6. So
<br> a) tn=3+(n-1).6=6n-3
<br> b) sn=n(3+n)/2
<br> c) if s=20, then n(n+3)/2=20, that is, n^2+3n-40=0.
<br> So n=5 or n=-8(discard). So n=5.
<br> d) If t=115,
<br> I am not sure if you state problem correctly, whether "t" is the same as tn, if so, there will not exist an n such that tn=115.
<br>
<br>5. In this sequence 2,6,10,...,626, a=2, d=4, and a(n)=626.
<br> So you can use a(n)=a+(n-1)d=4n-2=626
<br> Thus, n=628/4=157
<br>

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