Question

The recursive formula for an arithmetic sequence is given below. What is the fourth term in

the sequence?


A. -30
B. -18
C. -12
D. -24

Answer 1

B. -18

Explanation:

In order to find the fourth term of the sequence, first find second term, next, third term and finally fourth term.

`a_n = - 6 + a_((n - 1)) \\ \\ \implies \: a_2 = - 6 + a_((2 - 1)) = - 6 + a_1 = - 6 + 0 \\ \\ \implies \: \pink{a_2 = - 6} \\ \\\: a_3 = - 6 + a_((3 - 1)) = - 6 + a_2 = - 6 + ( - 6) \\ \\ \implies \: \purple{ a_3 = - 12}\\ \\\: a_4= - 6 + a_((4 - 1)) = - 6 + a_3 = - 6 + ( - 12) \\ \\ \implies \: \huge { \red{a_4 = - 18}}`

Another way:

`a_1=0`

`a_2=-6`(Calculated above)

`a_3=-6+a_2=-6-6=-12`

`a_4=-6+a_3=-6-12=-18`