Question

Find the 4th term in the sequence with the following definition:
A1= 0
An=2 (an-1 -3)

Answer 1

Answer:

A2=2(a2-1-3)

A2=2(a1-3)

A2=2(0-3)

A2=-6

A3=2(a2-3)

A3=2(-6-3)

A3=2*-9

A3=-18

A4=2(a3-3)

A4=2(-18-3)

A4=-42

Answer 2

The 4th term in the sequence using the given definition is -42.

for better understanding check the calcualtion below .

Calculation :

we find out the fourth term in the sequence by using the given formula

Given :

$a_1=0\\a_n=2(a_{n-1}-3)$

first term is given as 0

Lets find out the second term using the given formula

Substitute n =1 to find out second term

$a_n=2(a_{n-1}-3)\\n=2\\ a_2=2(a_{2-1}-3)\\ a_2=2(a_{1}-3)\\a_2=2(0-3)\\a_2=-6$

so the second term is -6

Find out thrid term by substituting n = 3

$a_3=2(a_2-3)\\a_3=2(-6-3)\\a_3=-18$

So the third term is -18 . Now find out fourth term by substituting 4 for n

$a_4=2(a_3-3)\\a_4=2(-18-3)\\a_4=-42$

The 4th term in the sequence using the given definition is -42

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