Question

Given that the first term is LaTeX: t_1=5t 1 = 5, and the recursive definition is LaTeX: t_{n+1}=3\cdot t_nt n + 1 = 3 ⋅ t n, what would be the second term (i.e. LaTeX: t_2t 2)

Group of answer choices

3

5

8

15

Answer 1

• Fourth choice: 15

Step-by-step explanation:

The question is: given that the first term is
`t_1=5` and the recursive definition is
`t_(n+1)=3\cdot t_n` , what would be the second term (i.e.
`t_2` )

A recursive defintion or recursive formula is an equation (a rule) that you apply over a term to find the next term, and so you can use it repeatedly to find the successive terms of a series.

In this case, your rule is that you multiply each term by 3, starting from 5.

Thus:

• First term:
  `t_1=5`

• Second term = 3 × first term :
  `t_2=3\cdot t_1=3\cdot 5=15`

Hence, your answer is 15 (the fourth choice).