Question

question
if ( a_1 = 4 ) and ( a_n = -4a_{n - 1} ) then find the value of ( a_6 ).

Explanation:

Step1: Find $a_2$ using $a_1$

$a_2 = -4a_1 = -4\times4 = -16$

Step2: Find $a_3$ using $a_2$

$a_3 = -4a_2 = -4\times(-16) = 64$

Step3: Find $a_4$ using $a_3$

$a_4 = -4a_3 = -4\times64 = -256$

Step4: Find $a_5$ using $a_4$

$a_5 = -4a_4 = -4\times(-256) = 1024$

Step5: Find $a_6$ using $a_5$

$a_6 = -4a_5 = -4\times1024 = -4096$

Answer:

$-4096$