WRITE THE FIRST 6 TERMS OF EACH PATTERN

About "Write the First 6 Terms of Each Pattern"

Write the First 6 Terms of Each Pattern :

Here we are going to see how to write first 6 terms of the given pattern.

Write the first 6 terms of the sequences whose nth term an is given below.

(i) an = n + 1 if n is odd

            n if n is even

Solution :

If n = 1

an  =  n + 1 

  =  1 + 1  =  2

If n = 3

an  =  n + 1 

  =  3 + 1  =  4

If n = 5

an  =  n + 1 

  =  5 + 1  =  6

If n = 2

an  =  n 

a2  =  2

If n = 4

an  =  n 

a4  =  4

If n = 6

an  =  n 

a6  =  6

Hence first 6 terms are 2, 2, 4, 4, 6,  6

Question 2 :

  an = 1 if n = 1

        2 if n = 2

an−1 + an−2 if n > 2

Solution :

1st term  =  1

2nd term  =  2

3rd term :

an = an−1 + an−2

a3 = a3−1 + a3−2  ==>  a2 + a==>  2 + 1  ==> 3

4th term :

an = an−1 + an−2

a4 = a4−1 + a4−2  ==>  a3 + a2  ==>  3 + 2  ==> 5

5th term :

an = an−1 + an−2

a5 = a5−1 + a5−2  ==>  a4 + a3  ==>  5 + 3  ==> 8

6th term :

an = an−1 + an−2

a6 = a6−1 + a6−2  ==>  a5 + a4  ==>  8 + 5  ==> 13

Hence the first 6 terms are 1, 2, 3, 5, 8 and 13.

Question 3 :

an =  n if n is 1, 2 or 3

         an−1 + an−2 + an−3 if n > 3

Solution :

1st term :

an =  n

a1 =  1

2nd term :

an =  n

a2 =  2

3rd term :

an =  n

a3 =  3

4th term :

an =  an−1 + an−2 + an−3

a4 =  a3 + a2 + a1  ==>  3 + 2 + 1  ==>  6

5th term :

an =  an−1 + an−2 + an−3

a5 =  a4 + a3 + a2  ==>  6 + 3 + 2  ==>  11

6th term :

an =  an−1 + an−2 + an−3

a6 =  a5 + a4 + a3  ==>  11 + 6 + 3  ==>  20

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