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10 cards from this deck
SnS_nSn
Sn=12n(a+ℓ)S_n = \frac{1}{2}n(a + \ell)Sn=21n(a+ℓ)
Sn=12n(2a+(n−1)d)S_n = \frac{1}{2}n(2a + (n-1)d)Sn=21n(2a+(n−1)d)
Sn=12n(a+ℓ)S_n = \frac{1}{2}n(a + \ell)Sn=21n(a+ℓ) (first formula)
(a+ℓ)(a + \ell)(a+ℓ) (first term + last term)
ℓ=Tn=a+(n−1)d\ell = T_n = a + (n-1)dℓ=Tn=a+(n−1)d
b−a+1b - a + 1b−a+1
Sum can eventually become negative
Use Tn=a+(n−1)dT_n = a + (n-1)dTn=a+(n−1)d, solve for nnn
Set up simultaneous equations to find aaa and ddd
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