Complete the given series by finding the missing term.
a b _ a _ b _ c c _ a a b b b _ _ c

a b c a b b

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c a b a c c

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c a b c b c

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c b b c a a

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Solution

The correct option is B c a b a c c
Here the number of times the letters repeat in successive terms is increasing
Thus the series is a b c a a b b c c a a a b b b cc c

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|\begin{matrix} b + c & c + a & a + b \\ c + a & a + b & b + c \\ a + b & b + c & c + a \end{matrix}| = 0

a + b + c = 0 or, a = b = c

a, b

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Δ = ∣ ∣ ∣ ∣ \begin{matrix} b + c & c + a & a + b c + a & a + b & b + c a + b & b + c & c + a \end{matrix} ∣ ∣ ∣ ∣ = 0

a + b + c = 0

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\frac{a {(b - c)}^{2}}{(c - a) (a - b)} + \frac{b {(c - a)}^{2}}{(a - b) (b - c)} + \frac{c {(a - b)}^{2}}{(b - c) (c - a)} = a + b + c

∣ ∣ ∣ ∣ \begin{matrix} b + c & a - c & a - b b - c & c + a & b - a c - b & c - a & a + b \end{matrix} ∣ ∣ ∣ ∣ =

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