Re: Sequence S is defined as a_n = (-1)^n(a_n – 1 + a_n – 2), where a_1 =
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11 Jul 2021, 05:57
According to the formula,
a_35 = - a_34 - a_33;
and
a_38 = a_37 + a_36;
Therefore,
a_35 + a_38 = a_35 + a_36 + a_37;
Notice that the required expression results in the sum of three consecutive terms: a_35 + a_36 + a_37;
If n is odd, then in the given formula reduces to:
a_n = - a_{n-1} - a_{n-2};
a_{n-2} + a_{n-1} + a_n = 0;
Therefore, if n is odd, then the sum of three consecutive terms in this sequence is 0.
In a_35 + a_36 + a_37;, n is 35 which is odd,
Therefore, a_35 + a_36 + a_37 = 0;
Therefore, the answer is B.