Consider the sequence of numbers a1- a2- a3- - to infinity where a 1-81-33 and a2-19 and aj-aj-1 aj-2- for j-3- What is the sum of the first 6002 terms of this sequence-CAT 2004A- -100-33B- 62-33C- 119-33D- -30

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Sum of n Terms

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Consider the sequence of numbers a₁, a₂, a₃,…. to infinity where a1 = 81.33 and a₂ = -19 and a_j = a_j _{– 1} a_j _{– 2} , for j >= 3. What is the sum of the first 6002 terms of this sequence?(CAT 2004)

-100.33

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-30

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62.33

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119.33

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a_{1}, a_{2}, a_{3} . . . .

a_{1}

a_{2}

a_{j} = a_{j - 1} - a_{j - 2}

\geq

a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}

\frac{5}{7} = \frac{a_{2}}{2!} + \frac{a_{3}}{3!} + \frac{a_{4}}{4!} + \frac{a_{5}}{5!} + \frac{a_{6}}{6!} + \frac{a_{7}}{7!}

0 \leq a_{j} < j

j = 2, 3, 4, 5, 6, 7

a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

(a_{1}, a_{2}, a_{3}, . . ., a_{2011})

j, k

1 \leq j < k \leq 2011

| a_{j} - j | = | a_{k} - k |

∣ ∣ ∣ ∣ ∣ \begin{matrix} (a - a_{1})^{- 2} & (a - a_{1})^{- 1} & a_{1}^{- 1} (a - a_{2})^{- 2} & (a - a_{2})^{- 1} & a_{2}^{- 1} (a - a_{3})^{- 2} & (a - a_{3})^{- 1} & a_{3}^{- 1} \end{matrix} ∣ ∣ ∣ ∣ ∣ = \pm \frac{a^{2} \prod (a_{i} - a_{j})}{\prod a_{i} \prod (a - a_{i})^{2}}

a_{1}, a_{2}, a_{3}, . .

a_{n + 1}^{2} = a_{n} a_{n + 2} + (- 1)^{n}

a_{3}

a_{1} = 2

a_{2} = 5

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