Write the first four terms of the sequence defined by the recursion formula.
a1 = 6 and an = 3an-1 for n ≥ 2
The recursive formula for a sequence is an = 3an – 1; a1 = –1. What is the 4th term of the sequence?
6 18 54 162
To find the first four terms of the sequence defined by the recursion formula, we can use the given formula:
a1 = 6
an = 3 * an-1
Step 1: Find a2
Using the recursive formula, we have:
a2 = 3 * a1 = 3 * 6 = 18
Step 2: Find a3
Using the recursive formula, we have:
a3 = 3 * a2 = 3 * 18 = 54
Step 3: Find a4
Using the recursive formula, we have:
a4 = 3 * a3 = 3 * 54 = 162
Therefore, the first four terms of the sequence are:
a1 = 6
a2 = 18
a3 = 54
a4 = 162
To find the first four terms of the sequence defined by the recursion formula, we can use the given formula:
a1 = 6 (given)
an = 3an-1 for n ≥ 2
Let's calculate the first four terms step by step:
First term (n = 1):
a1 = 6
Second term (n = 2):
a2 = 3a1
= 3(6)
= 18
Third term (n = 3):
a3 = 3a2
= 3(18)
= 54
Fourth term (n = 4):
a4 = 3a3
= 3(54)
= 162
Therefore, the first four terms of the sequence are:
a1 = 6
a2 = 18
a3 = 54
a4 = 162