Question

Find the 4th term if the sequend in which a1 = 2 and a n+1 = -4a n + 2

Answer 1

$a_n_+_1=-4a_n_+_2$

dividing both sides by -4, we get:

$a_n_+_2=- \frac{a_n_+_1}{4}$

this means, each term is its previous term divided by -4.

now we can construct the sequence as follows:

$a_1=2$

$a_2=- \frac{a_1}{4}= - \frac{2}{4}= -\frac{1}{2}$

$a_3=- \frac{a_2}{4} =- \frac{ \frac{1}{2} }{4}=- \frac{1}{8}$

$a_4=- \frac{a_3}{4}=- \frac{ \frac{1}{8} }{4}=- \frac{1}{32}$



Answer: the last term is -1/32