Question

Plz do both of them for me and even show the work plzzzzzz

Answer 1

(a)= option 3

(b)= option 3

Explanation:

(A) It is given that a sequence is defined by the recursive function
`a_(1)=1` and
`a_(n)=a_(n-1)+n`

Now, substituting the value of n=2 in above equation,

`a_(2)=a_(1)+2`

`a_(2)=1+2`

`a_(2)=3`

Again putting n=3,

`a_(3)=a_(2)+3`

`a_(3)=3+3`

`a_(2)=6`

Putting n=4,

`a_(4)=a_(3)+4`

`a_(4)=6+4`

`a_(4)=10`

Putting n=5,

`a_(5)=a_(4)+5`

`a_(5)=10+5`

`a_(5)=15`

Putting n=6,

`a_(6)=a_(5)+6`

`a_(6)=15+6`

`a_(6)=21`

Putting n=7,

`a_(7)=a_(6)+7`

`a_(7)=21+7`

`a_(7)=28`

Hence, option 3 is correct.

(B) The given sequence is :

5, -10, 20, -40, 80.....

Since, the given sequence is GP, therefore

`a_(1)=5` and r=-2

The nth term is given by:

`a_(n)=a_(1)r^(n-1)`

For fifteenth term, put n=15 in above equation, we get

`a_(15)=5(-2)^(14)`

=
`5{*}16384`

=
`81920`

Hence, the fifteenth term is 81920.

Option 3 is correct.