Here we are going to see some practice questions to find the nth term of the sequence.

How to find nth term of the sequence ?

There is some arrangement or pattern followed in every sequence. We find nth term of the sequence in term of n. By applying the position value of n in the nth term, we must get the value in that particular place.

For example, by applying 5 instead of n in nth term, we get the 5th term of the sequence.

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 1 :

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

(i) a_{n} = 5n / (n + 2); a_{6} and a_{13}

Solution :

To find a_{6}, we have to apply 6 instead of n.

To find a_{13}, we have to apply 13 instead of n.

a_{n} = 5n / (n + 2)

n = 6

a_{6} = 5(6)/(6 + 2)

= 30/8

a_{6} = 15/4

a_{n} = 5n / (n + 2)

n = 13

a_{13} = 5(13)/(13 + 2)

= 65/15

a_{13} = 13/3

(ii) a_{n } = -(n^{2} - 4); a_{4} and a_{11}

Solution :

To find a_{4}, we have to apply 4 instead of n.

To find a_{11}, we have to apply 11 instead of n.

a_{n} = -(n^{2} - 4)

n = 4

a_{4} = -(4^{2} - 4)

a_{4} = -(16 - 4)

= -12

a_{n} = -(n^{2} - 4)

n = 11

a_{11} = -(11^{2} - 4)

a_{11} = -(121 - 4)

= -117

After having gone through the stuff given above, we hope that the students would have understood, "Finding nth Term of the Sequence".

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