Question

A_(1)=5 and a_(n)=3a_(n-1) What is the value of term a_(4) ?

Answer 1

The fourth term of the sequence a_n, where a_1 is 5 and each term is three times the previous term, is calculated to be 135 by recursively applying the formula three times.

Step-by-step explanation:

The question requires us to calculate the fourth term of a sequence a_n where the first term a_1 is given as 5 and the recursion formula is a_n = 3a_{n-1}. To find a_4, we will apply the recursive formula three times starting with a_1.

1. a_2 = 3 × a_1 = 3 × 5 = 15
2. a_3 = 3 × a_2 = 3 × 15 = 45
3. a_4 = 3 × a_3 = 3 × 45 = 135

Therefore, the value of a_4 is 135.