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aleksklad [387]
3 years ago
10

Consider the sequence defined recursively by do = 0, an = an-1 + 3n – 1. a) Write out the first 5 terms of this sequence,

Mathematics
1 answer:
creativ13 [48]3 years ago
5 0

Answer:

The first 5 terms of the sequence is 2,7,15,26,40.

Step-by-step explanation:

Given : Consider the sequence defined recursively by a_0=0 a_n=a_{n-1}+3n-1

To find : Write out the first 5 terms of this sequence ?

Solution :

a_n=a_{n-1}+3n-1 and a_0=0

The first five terms in the sequence is at n=1,2,3,4,5

For n=1,

a_1=a_{1-1}+3(1)-1

a_1=a_{0}+3-1

a_1=0+2

a_1=2

For n=2,

a_2=a_{2-1}+3(2)-1

a_2=a_{1}+6-1

a_2=2+5

a_2=7

For n=3,

a_3=a_{3-1}+3(3)-1

a_3=a_{2}+9-1

a_3=7+8

a_3=15

For n=4,

a_4=a_{4-1}+3(4)-1

a_4=a_{3}+12-1

a_4=15+11

a_4=26

For n=5,

a_5=a_{5-1}+3(5)-1

a_5=a_{4}+15-1

a_5=26+14

a_5=40

The first 5 terms of the sequence is 2,7,15,26,40.

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-------------------------------------------------------------------------------------------------------------

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