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love history [14]
3 years ago
5

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

Mathematics
1 answer:
Vinvika [58]3 years ago
5 0

Answer:

(a)= option 3

(b)= option 3

Step-by-step 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{\times}16384

=81920

Hence, the fifteenth term is 81920.

Option 3 is correct.

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