Question

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

Answer 1

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

Explanation:

The sequence is defined recursively by the formula
`a_n=2*(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*(a_(2-1))+4`.

`\Rightarrow a_2=2*(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*(a_(3-1))+4`.

`\Rightarrow a_3=2*(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*(a_(4-1))+4`.

`\Rightarrow a_4=2*(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*(a_(5-1))+4`.

`\Rightarrow a_5=2*(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