WRITE THE FIRST 6 TERMS OF EACH PATTERN

Write the first 6 terms of the sequences whose n^th term an is given below.

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

            n if n is even

Solution :

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

Question 2 :

  a_n = 1 if n = 1

        2 if n = 2

a_n−1 + a_n−2 if n > 2

Solution :

1st term  =  1

2nd term  =  2

3^rd term :

a_n = a_n−1 + a_n−2

a₃ = a₃₋₁ + a₃₋₂  ==>  a₂ + a₁  ==>  2 + 1  ==> 3

4^th term :

a_n = a_n−1 + a_n−2

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

5^th term :

a_n = a_n−1 + a_n−2

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

6^th term :

a_n = a_n−1 + a_n−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 :

a_n =  n if n is 1, 2 or 3

         a_n−1 + a_n−2 + a_n−3 if n > 3

Solution :

4^th term :

a_n =  a_n−1 + a_n−2 + a_n−3

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

5^th term :

a_n =  a_n−1 + a_n−2 + a_n−3

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

6^th term :

a_n =  a_n−1 + a_n−2 + a_n−3

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

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