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

Answer:

• Fourth choice: 15

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).