Determine first five terms of sequence?

Question

Find the first five terms of the sequence:

I think that is is 2, -2, -6, -10, -14. Am I right?

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Answer 1 · 2017-12-08T13:12:58

Correct first five terms of series are $2, - 6, 2, - 6, 2$ $2,-6,2,-6,2$

As $a_{1} = 2$ $a_1=2$ , using $a_{n} = - a_{n - 1} - 4$ $a_n=-a_(n-1)-4$

$a_{2} = - a_{2 - 1} - 4 = - a_{1} - 4 = - 2 - 4 = - 6$ $a_2=-a_(2-1)-4=-a_1-4=-2-4=-6$

$a_{3} = - a_{3 - 1} - 4 = - a_{2} - 4 = - (- 6) - 4 = 6 - 4 = 2$ $a_3=-a_(3-1)-4=-a_2-4=-(-6)-4=6-4=2$

$a_{4} = - a_{4 - 1} - 4 = - a_{3} - 4 = - 2 - 4 = - 6$ $a_4=-a_(4-1)-4=-a_3-4=-2-4=-6$

$a_{5} = - a_{5 - 1} - 4 = - a_{4} - 4 = - (- 6) - 4 = 6 - 4 = 2$ $a_5=-a_(5-1)-4=-a_4-4=-(-6)-4=6-4=2$

Hence, correct first five terms of series are $2, - 6, 2, - 6, 2$ $2,-6,2,-6,2$