Question

What is the 4th term of the sequence a1=5 and an=3a_n-1?

A) 5
B) 15
C) 45
D) 135

Answer 1

The 4th term of the sequence defined by a1=5 and an=3a_n-1 is 135, found by successively multiplying the previous term by 3.

Step-by-step explanation:

We are asked to find the 4th term of the sequence given by a1=5 and an=3a_n-1. This is a geometric sequence where each term after the first is found by multiplying the previous term by 3. Let's calculate the terms step by step:

1. The first term (a1) is already given as 5.
2. The second term (a2) will be 3 multiplied by the first term, which is 3 * 5 = 15.
3. The third term (a3) is 3 multiplied by the second term, so 3 * 15 = 45.
4. Finally, the fourth term (a4) is 3 multiplied by the third term, which is 3 * 45 = 135.

Therefore, the 4th term of the sequence (a4) is 135.