# HOW TO FIND THE INDICATED TERM FROM GIVEN NTH TERM OF THE SEQUENCE

How to find the indicated term from given nth term of the sequence ?

Here we are going to see how to find the indicated term from given nth term of the sequence

• To find the indicated term, we have to apply the indicated number instead of n.
• For example, if we want to find 5th term of the sequence, we have to apply 5 instead of n in the nth term of the sequence.

Let us look into some example problems to understand the above concept.

Example 1 :

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

an  =  (n + 2)/(2n + 3);     a7 and a9

Solution :

In order to find 7th term and 9th term, we have to apply 7 and 9 instead of n in the given nth term of the sequence.

 7th terman  =  (n + 2)/(2n + 3)n = 7a7  =  (7 + 2)/(2(7) + 3)a7  =  9/(14 + 3)a7  =  9/17 9th terman  =  (n + 2)/(2n + 3)n = 9a9  =  (9 + 2)/(2(9) + 3)a9  =  11/(18 + 3)a9  =  11/21

Example 2 :

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

an  =  (-1)n 2n + 3(n + 1);     a5 and a8

Solution :

In order to find 5th term and 8th term, we have to apply 5 and 8 instead of n in the given nth term of the sequence.

 5th terman  =  (-1)n 2n + 3(n + 1)n = 5a5  =  (-1)5 25 + 3(5+1)a7  =  -1 ⋅ 28⋅ (6)a7  =  -1 ⋅ (256)⋅ (6)a7  =  - 1536 8th terman  =  (-1)n 2n + 3(n + 1)n  =  8a8  =  (-1)8 28 + 3(8+1)=  1 ⋅ 211 ⋅ (9)a8  =  1 ⋅ (2048) ⋅ (9)a8  =  18432

Example 3 :

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

an  =  2n2 - 3n + 1;  a5 and a7

Solution :

In order to find 5th term and 7th term, we have to apply 5 and 7 instead of n in the given nth term of the sequence.

 5th terman  =  2n2 - 3n + 1n = 5a5  =  2n2 - 3n + 1a5  =  2(5)2 - 3(5) + 1a5  =  2(25) - 15 + 1a5  =  50 - 15 + 1a5  =  51 - 15a5  =  36 7th terman  =  (-1)n 2n + 3(n + 1)n  =  8a7  =  2n2 - 3n + 1a7  =  2(7)2 - 3(7) + 1a7  =  2(49) - 21 + 1a7  =  98 - 21 + 1a7  =  99 - 21=  78

Example 4 :

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

an  =  (-1)n (1 - n + n2);  a5 and a8

Solution :

In order to find 5th term and 8th term, we have to apply 5 and 8 instead of n in the given nth term of the sequence.

 5th terman  =  (-1)n (1 - n + n2)n = 5an  =  (-1)5 (1 - 5 + 52)a5  =  (-1)(1 - 5 + 25)a5  =  (-1)(26 - 5)a5  =  -21 8th terman  =  (-1)n (1 - n + n2)n = 8an  =  (-1)8 (1 - 8 + 82)a8  =  1 (1 - 8 + 64)a8  =  (65 - 8)a8  =  57

After having gone through the stuff given above, we hope that the students would have understood how to find the indicated term from given nth term of the sequence.

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