Question

Given The recourse recursive formula, find the first four terms:

Answer 1

Explanation:

hence,

the first four terms are 45,-135,405,-1215

Answer 2

c

Explanation:

we are given that

`\displaystyle a_(n) = - 3 \: \cdot a_(n - 1) \\ a_(1) = 45`

we are already given our first term i.e 45

for second term

`\displaystyle a_(2) = - 3 \: \cdot a_(2- 1)`

simplify substraction:

`\displaystyle a_(2) = - 3 \: \cdot a_(1)`

since we have
`a_1=45`

substitute:

`\displaystyle a_(2) = - 3 \: \cdot 45`

simplify multiplication:

`\displaystyle a_(2) = - 135`

for third term

`\displaystyle a_(3) = - 3 \: \cdot a_(3- 1)`

simplify Substraction:

`\displaystyle a_(3) = - 3 \: \cdot a_(2)`

as
`a_2=-135`

substitute:

`\displaystyle a_(3) = - 3 \: \cdot - 135`

simplify multiplication:

`\displaystyle a_(3) = 405`

for forth term

`\displaystyle a_(2) = - 3 \: \cdot a_(4- 1)`

simplify Substraction:

`\displaystyle a_(2) = - 3 \: \cdot a_(3)`

substitute:

`\displaystyle a_(2) = - 3 \: \cdot 405`

simplify multiplication:

`\displaystyle a_(2) = - 1215`

hence,

the first four terms are 45,-135,405,-1215