HOW TO FIND THE NTH TERM OF A SEQUENCE

Write the nth term of the following sequences ;

Example 1 :

2, 2, 4, 4, 6, 6, ........

Solution :

By observing the given sequence first, second terms are same, third and fourth terms are same and so on.

To find nth term of the sequence, let us divide them into two parts.

Hence t_n = n + 1  (if n is odd)

               = n (if n is even)

Example 2 :

1/2 , 2/3 , 3/4 , 4/5 , 5/6, ........

Solution :

By observing the given sequence, the numerator is 1 lesser than the denominator.

Let t_n  =  n/(n+1) 

t₁  =  1/(1+1)  ==>  1/2

t₂  =  2/(2+1)  ==>  2/3

t₃  =  3/(3+1)  ==>  3/4

Hence the required nth term of the given sequence is n/(n+1).

Example 3 :

1/2, 3/4, 5/6, 7/8, 9/10, ........

Solution :

By observing the given sequence, the numerator is 1 lesser than the denominator and they are odd terms.

Let t_n  =  (2n-1)/2n

t₁  =  (2(1) - 1)/2(1) ==>  1/2

t₂  =  (2(2) - 1)/2(2) ==>  3/4

t₃  =  (2(3) - 1)/2(3) ==>  5/6

Hence the required nth term of the given sequence is (2n-1)/2n.

Example 4 :

6, 10, 4, 12, 2, 14, 0, 16, −2, ........

Solution :

By observing the given sequence first, second terms are same, third and fourth terms are same and so on.

To find nth term of the sequence, let us divide them into two parts.

Hence the nth term is 

t_n = 7 - n  (if n is odd) 

    = 8 + n  (if n is even)

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