## HOW TO FIND THE NTH TERM OF THE ARITHMETIC SEQUENCE

How to find the nth term of the arithmetic sequence :

To find the nth term of the arithmetic sequence, we use the formula given below.

an  =  a + (n - 1)d

Let us look into some example problems to understand how to find the nth term of the arithmetic sequence.

Example 1 :

Find the nth term of each arithmetic sequence described.

a1 = 5, d = 5, n = 25

Solution :

Applying the given values in the formula

an  =  a + (n - 1)d

we get,

a25  =  5 + (25-1)(5)

a25  =  5 + 24(5)

a25  =  5 + 120

a25  =  125

Hence 25th term of the above sequence is 125.

Example 2 :

Find the nth term of each arithmetic sequence described.

a1 = 8, d = 3, n = 16

Solution :

Applying the given values in the formula

an  =  a + (n - 1)d

we get,

a16  =  8 + (16-1)(3)

a16  =  8 + 15(3)

a16  =  8 + 45

a16  =  53

Hence 16th term of the above sequence is 53.

Example 3 :

Find the nth term of each arithmetic sequence described.

a1 = 34, d = 15, n = 200

Solution :

Applying the given values in the formula

an  =  a + (n - 1)d

we get,

a200  =  34 + (200-1)(15)

a200  =  34 + 195(15)

a200  =  34 + 2925

a200  =  2959

Hence 200th term of the above sequence is 2959.

Example 4 :

Find the nth term of each arithmetic sequence described.

a1 = 5/8, d = 1/8, n = 22

Solution :

Applying the given values in the formula

an  =  a + (n - 1)d

we get,

a22  =  (5/8) + (22-1)(1/8)

a22  =  (5/8) + 21(1/8)

a22  =  (5/8) + 21/8

a22  =  (21 + 5)/8

=  26/8

=  13/4

Hence 22nd term of the above sequence is 13/4.

Example 5 :

Find the nth term of each arithmetic sequence described.

a1 = 3/2, d = 9/4, n = 39

Solution :

Applying the given values in the formula

an  =  a + (n - 1)d

we get,

a39  =  (3/2) + (39-1)(9/4)

a39  =  (3/2) + 38(9/4)

a39  =  (3/2) + 171/2

a39  =  (171+3)/2

=  174/2

=  87

Hence 39th term of the above sequence is 87.

Let us see the next example on "How to find the nth term of the arithmetic sequence".

Example 6 :

Find the nth term of each arithmetic sequence described.

0.5, 1, 1.5, 2, … for n = 50

Solution :

Applying the given values in the formula

an  =  a + (n - 1)d

a  =  0.5, d  =  1 - 0.5 = 0.5

we get,

a50  =  0.5 + (50-1)(0.5)

a50  =  0.5 + 49(0.5)

a50  =  0.5 + 24.5

a50  =  25

Hence 50th term of the above sequence is 25.

After having gone through the stuff given above, we hope that the students would have understood "How to find the nth term of the arithmetic sequence".

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