Question

Последовательности (Сn) задана условиями c1=6, cn+1=(-1)^n+1 cn-4. Найдите C4.Помогите пожалуйста.с объяснением !!!!! ^^

Answer 1

$c_1=6,\; \; \; c_{n+1}=(-1)^{n+1}\cdot c_{n}-4\\\\n\; \; -\; \; nomer \; (!)\\\\c_2=(-1)^{1+1}\cdot c_1-4=(-1)^{2}\cdot 6-4=6-4=2\\\\c_3=(-1)^{2+1}\cdot c_2-4=(-1)^3\cdot 2-4=-2-4=-6\\\\c_4=(-1)^{3+1}\cdot c_3-4=(-1)^4\cdot (-6)-4=-6-4=-10$

Answer 2

Finding C4 in the Sequence (Cn)

To find the value of C4 in the sequence (Cn) defined by the conditions c1 = 6 and cn+1 = (-1)^(n+1) + cn - 4, we can use the given recursive formula to calculate the terms of the sequence until we reach C4.

Let's calculate the terms of the sequence step by step:

- c1 = 6 (given) - c2 = (-1)^(2+1) + c1 - 4 = -1 + 6 - 4 = 1 - c3 = (-1)^(3+1) + c2 - 4 = 1 + 1 - 4 = -2 - c4 = (-1)^(4+1) + c3 - 4 = -1 + (-2) - 4 = -7

Therefore, C4 = -7.

Note: The calculations above are based on the given recursive formula and do not require any external sources for verification.