Nth TERM OF AN ARITHMETIC SEQUENCE

Find the n^th nth term of each arithmetic sequence.

Example 1 :

-3, -6, -9, -12, ......

Solution :

In the given arithmetic sequence

a₁ = -3

d = a₂ - a₁

= -6 - (-3)

= -6 + 3

= -3

Formula to find n^th term of an arithmetic sequence :

a_n = a₁ + (n - 1)d

Substitute a₁ = -3 and d = -3.

a_n = -3 + (n - 1)(-3)

a_n = -3 - 3n + 3

a_n = -3n

Example 2 :

8, 9, 10, 11, ......

Solution :

In the given arithmetic sequence

a₁ = 8

d = a₂ - a₁

= 9 - 8

= 1

Formula to find n^th term of an arithmetic sequence :

a_n = a₁ + (n - 1)d

Substitute a₁ = 8 and d = 1.

a_n = 8 + (n - 1)(1)

a_n = 8 + n - 1

a_n = n + 7

Example 3 :

2, 8, 14, 20, ......

Solution :

In the given arithmetic sequence

a₁ = 2

d = a₂ - a₁

= 8 - 2

= 6

Formula to find n^th term of an arithmetic sequence :

a_n = a₁ + (n - 1)d

Substitute a₁ = 2 and d = 6.

a_n = 2 + (n - 1)(6)

a_n = 2 + 6n - 6

a_n = 6n - 4

Example 4 :

-18, -16, -14, -12, ......

Solution :

In the given arithmetic sequence

a₁ = -18

d = a₂ - a₁

= -16 - (-18)

= -16 + 18

= 2

Formula to find n^th term of an arithmetic sequence :

a_n = a₁ + (n - 1)d

Substitute a₁ = -18 and d = 2.

a_n = -18 + (n - 1)(2)

a_n = -18 + 2n - 2

a_n = 2n - 20

Example 5 :

12, 23, 34, 45, ......

Solution :

In the given arithmetic sequence

a₁ = 23

d = a₂ - a₁

= 23 - 12

= 11

Formula to find n^th term of an arithmetic sequence :

a_n = a₁ + (n - 1)d

Substitute a₁ = 12 and d = 11.

a_n = 12 + (n - 1)(11)

a_n = 12 + 11n - 11

a_n = 11n - 1

Example 6 :

9, 17, 25, 33, ......

Solution :

In the given arithmetic sequence

a₁ = 9

d = a₂ - a₁

= 17 - 9

= 8

Formula to find n^th term of an arithmetic sequence :

a_n = a₁ + (n - 1)d

Substitute a₁ = 9 and d = 8.

a_n = 9 + (n - 1)(8)

a_n = 9 + 8n - 8

a_n = 8n + 1

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