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

Plz do both of them for me and even show the work plzzzzzz-example-1
User Kidnim
by
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1 Answer

3 votes

Answer:

(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.

User Leonardo Ferreira
by
8.2k points

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