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

To find the indicated term of a sequence, substitute the given value for n.

For example, if you want to find 5^th term of a sequence, substitute n = 5 in the n^th term of the sequence.

Example 1 :

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

a_n = (n + 2)/(2n + 3); a₇ and a₉

Solution :

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

7^th term

a_n = (n + 2)/(2n + 3)

n = 7

a₇ = (7 + 2)/(2(7) + 3)

a₇ = 9/(14 + 3)

a₇ = 9/17

9^th term

a_n = (n + 2)/(2n + 3)

n = 9

a₉ = (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

a_n = (-1)ⁿ 2^{n + 3}(n + 1); a₅ and a₈

Solution :

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

5^th term

a_n = (-1)ⁿ 2^{n + 3}(n + 1)

n = 5

a₅ = (-1)⁵ 2^{5 + 3}(5+1)

a₇ = -1 ⋅ 2⁸⋅ (6)

a₇ = -1 ⋅ (256)⋅ (6)

a₇ = - 1536

8^th term

a_n = (-1)ⁿ 2^{n + 3}(n + 1)

n = 8

a₈ = (-1)⁸ 2^{8 + 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

a_n = 2n² - 3n + 1; a₅ and a₇

Solution :

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

5^th term

a_n = 2n² - 3n + 1

n = 5

a₅ = 2n² - 3n + 1

a₅= 2(5)² - 3(5) + 1

a₅= 2(25) - 15 + 1

a₅= 50 - 15 + 1

a₅= 51 - 15

a₅= 36

7^th term

a_n = (-1)ⁿ 2^{n + 3}(n + 1)

n = 8

a₇ = 2n² - 3n + 1

a₇ = 2(7)² - 3(7) + 1

a₇ = 2(49) - 21 + 1

a₇ = 98 - 21 + 1

a₇ = 99 - 21

= 78

Example 4 :

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

a_n = (-1)ⁿ (1 - n + n²); a₅ and a₈

Solution :

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

5^th term

a_n = (-1)ⁿ (1 - n + n²)

n = 5

a_n = (-1)⁵ (1 - 5 + 5²)

a₅= (-1)(1 - 5 + 25)

a₅= (-1)(26 - 5)

a₅= -21

8^th term

a_n = (-1)ⁿ (1 - n + n²)

n = 8

a_n = (-1)⁸ (1 - 8 + 8²)

a₈= 1 (1 - 8 + 64)

a₈= (65 - 8)

a₈= 57

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

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