FINDING nth TERM OF A SEQUENCE

Question 1 :

Find the nth term of the following sequences

(i) 2, 5, 10, 17,...

Solution :

(1 + 1), (4 + 1), (9 + 1), (16 + 1),...

(1² + 1), (2² + 1), (3² + 1), (4² + 1),...

nth term of the sequence  :

a_n  =  n² + 1

(ii) 0, 1/2, 2/3, ............

Solution :

Denominator is 1 more than the numerator. By approaching the above problem in this way, we will not get the first term.

Numerator is 1 less than the denominator.

  =  0, 1/2, 2/3, ............

  =  (1-1)/1, (2-1)/2, (3-1)/3, ...................

nth term of the sequence is (n - 1)/n

(iii) 3, 8, 13, 18,...

Solution :

  =  3, 8, 13, 18,...

we may see the common things followed in each term.

  =  (5 - 2), (10 - 2), (15 - 2), (20 - 2),...

nth term of the sequence is 5n - 2.

Finding the Indicated Term of a Sequence ?

Question 2 :

Find the indicated terms of the sequences whose nth terms are given by

(i) a_n  =  5n / (n + 2); a₆ and a₁₃

Solution :

To find a₆, we have to apply 6 instead of n.

To find a₁₃, we have to apply 13 instead of n.

(ii) a_n  =  -(n² - 4); a₄ and a₁₁

Solution :

To find a₄, we have to apply 4 instead of n.

To find a₁₁, we have to apply 11 instead of n.

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