Question

.Write the first five terms of the sequence defined by the recursive formula

Answer 1

Answer:

The first five terms are $-1,2,8,20,44$.

Step-by-step explanation:

The sequence is defined recursively by the formula $a_n=2\times(a_{n-1})+4$.

The first term of the sequence is given to be, $a_1=-1$.

To find the next term, we substitute $n=2$ in to the above formula to get,

$a_2=2\times(a_{2-1})+4$.

$\Rightarrow a_2=2\times(a_{1})+4$.

But $a_1=-1$

$\Rightarrow a_2=2(-1)+4$.

$\Rightarrow a_2=-2+4$.

$\Rightarrow a_2=2$.

To find the third term, we substitute $n=3$ in to the above formula to get,

$a_3=2\times(a_{3-1})+4$.

$\Rightarrow a_3=2\times(a_{2})+4$.

But $a_2=2$

$\Rightarrow a_3=2(2)+4$.

$\Rightarrow a_3=4+4$.

$\Rightarrow a_3=8$.

To find the fourth term, we substitute $n=4$ in to the above formula to get,

$a_4=2\times(a_{4-1})+4$.

$\Rightarrow a_4=2\times(a_{3})+4$.

But $a_3=8$

$\Rightarrow a_4=2(8)+4$.

$\Rightarrow a_4=16+4$.

$\Rightarrow a_4=20$.

To find the fifth term, we substitute $n=5$ in to the above formula to get,

$a_5=2\times(a_{5-1})+4$.

$\Rightarrow a_5=2\times(a_{4})+4$.

But $a_4=20$

$\Rightarrow a_5=2(20)+4$.

$\Rightarrow a_5=40+4$.

$\Rightarrow a_5=44$.

Therefore, the first five terms are $-1,2,8,20,44$. The correct answer is C