**Finding the nth term of an arithmetic sequence worksheet :**

Here we are going to see some practice questions on finding the nth term of an arithmetic sequence.

(1) Find the n^{th} term of each arithmetic sequence described.

a_{1} = 5, d = 5, n = 25

(2) Find the n^{th} term of each arithmetic sequence described.

a_{1} = 8, d = 3, n = 16

(3) Find the n^{th} term of each arithmetic sequence described.

a_{1} = 34, d = 15, n = 200

(4) Find the n^{th} term of each arithmetic sequence described.

a_{1} = 5/8, d = 1/8, n = 22

(5) Find the n^{th} term of each arithmetic sequence described.

a_{1} = 3/2, d = 9/4, n = 39

(6) Find the n^{th} term of each arithmetic sequence described.

0.5, 1, 1.5, 2, … for n = 50

**Example 1 :**

Find the n^{th} term of each arithmetic sequence described.

a_{1} = 5, d = 5, n = 25

**Solution :**

Applying the given values in the formula

a_{n} = a + (n - 1)d

we get,

a_{25} = 5 + (25-1)(5)

a_{25} = 5 + 24(5)

a_{25} = 5 + 120

a_{25} = 125

Hence 25^{th} term of the above sequence is 125.

**Example 2 :**

Find the n^{th} term of each arithmetic sequence described.

a_{1} = 8, d = 3, n = 16

**Solution :**

Applying the given values in the formula

a_{n} = a + (n - 1)d

we get,

a_{16} = 8 + (16-1)(3)

a_{16} = 8 + 15(3)

a_{16} = 8 + 45

a_{16} = 53

Hence 16^{th} term of the above sequence is 53.

**Example 3 :**

Find the n^{th} term of each arithmetic sequence described.

a_{1} = 34, d = 15, n = 200

**Solution :**

Applying the given values in the formula

a_{n} = a + (n - 1)d

we get,

a_{200} = 34 + (200-1)(15)

a_{200} = 34 + 195(15)

a_{200} = 34 + 2925

a_{200} = 2959

Hence 200^{th} term of the above sequence is 2959.

**Example 4 :**

Find the n^{th} term of each arithmetic sequence described.

a_{1} = 5/8, d = 1/8, n = 22

**Solution :**

Applying the given values in the formula

a_{n} = a + (n - 1)d

we get,

a_{22} = (5/8) + (22-1)(1/8)

a_{22} = (5/8) + 21(1/8)

a_{22} = (5/8) + 21/8

a_{22} = (21 + 5)/8

= 26/8

= 13/4

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

**Example 5 :**

Find the n^{th} term of each arithmetic sequence described.

a_{1} = 3/2, d = 9/4, n = 39

**Solution :**

Applying the given values in the formula

a_{n} = a + (n - 1)d

we get,

a_{39} = (3/2) + (39-1)(9/4)

a_{39} = (3/2) + 38(9/4)

a_{39} = (3/2) + 171/2

a_{39} = (171+3)/2

= 174/2

= 87

Hence 39^{th} 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 n^{th} term of each arithmetic sequence described.

0.5, 1, 1.5, 2, … for n = 50

**Solution :**

Applying the given values in the formula

a_{n} = a + (n - 1)d

a = 0.5, d = 1 - 0.5 = 0.5

we get,

a_{50} = 0.5 + (50-1)(0.5)

a_{50} = 0.5 + 49(0.5)

a_{50} = 0.5 + 24.5

a_{50} = 25

Hence 50^{th} term of the above sequence is 25.

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