Question

which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an=-2+(n-1)3

Answer 1

Answer:

$a_{n} = a_{n-1} + 3$ and $a_{1} = -2$

Step-by-step explanation:

The terms of an arithmetic sequence are given by the formula

$a_{n} = -2 + (n - 1)3 = 3n - 5$

So, the first term, $a_{1} = 3(1) - 5 = - 2$

The second term, $a_{2} = 3(2) - 5 = 1$

The third term, $a_{3} = 3(3) - 5 = 4$

And the fourth term, $a_{4} = 3(4) - 5 = 7$

So, from the terms of the A.P. sequence, it is clear that,

$a_{n} = a_{n-1} + 3$ and $a_{1} = -2$

Therefore, this is the recursive formula of the given arithmetic sequence. (Answer)