**How to find the specified term of an arithmetic sequence ?**

The formula to find n^{th} term is

**a _{n} = a + (n - 1)d**

**Question 1 :**

Find the common difference and 15^{th} term of an A.P

125, 120, 115, 110, ……….….

**Solution :**

First term (a) = 125

Common difference (d) = a_{2} – a_{1}

d = 120 – 125

d = -25

General term of an A.P

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

a_{n} = 125 + (15 - 1) (-25)

a_{n} = 125 + 14 (-25)

a_{n} = 125 – 350

a_{15} = -225

Therefore 15^{th} term of A.P is -225

**Question 2 :**

Which term of the arithmetic sequence is

24 , 23 ¼ ,22 ½ , 21 ¾ , ………. is 3?

**Solution :**

First term (a) = 24

Common difference (d) = a_{2} – a_{1}

d = 23 ¼ – 24

d = (93/4) – 24

d = -3/4

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

Let us consider 3 as n^{th} term

a_{n} = 3

3 = 24 + (n-1) (-3/4)

3 – 24 = (n-1) (-3/4)

(-21 ⋅ 4)/(-3) = n -1

84/3 = n -1

28 = n – 1

n = 29

Hence 3 is the 29^{th} term of A.P.

**Question 3 :**

Find the 12^{th} term of the A.P

√2 , 3 √2 , 5 √2 , …………

**Solution :**

First term (a) = √2

Common difference = 3 √2 - √2

d = 2 √2

n = 12

General term of an A.P

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

a_{12} = √2 + (12 - 1) (2√2)

= √2 + 11 (2√2)

= √2 + 22 √2

= 23 √2

Hence 12^{th} of A.P is 23 √2.

**Question 4 :**

Find the 17^{th} term of the A.P

4 , 9 , 14 ,…………

**Solution :**

First term (a) = 4

Common difference (d) = 9 - 4

d = 5

n = 17

General term of an A.P

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

a_{17} = 4 + (17 - 1) (5)

a_{17 } = 4 + 16 (5)

a_{17 } = 84

Hence 17^{th} of A.P is 84

**Question 5 :**

The 10^{th} and 18^{th} terms of an A.P are 41 and 73 respectively. Find the 27^{th} term

**Solution :**

10th term = 41

a + 9 d = 41 ------- (1)

18th term = 73

a + 17 d = 73 ------- (2)

Subtracting (2) from (1)

a + 17 d - (a + 9 d) = 73 - 41

a + 17d - a - 9d = 32

8d = 32

d = 4

By substituting the value of d in (1)

a + 9 (4) = 41

a + 36 = 41

a = 5

Now, we have to find 27^{th} term

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

here n = 27

a_{27} = 5 + (27-1) 4

a_{27 }= 5 + 26 (4)

a_{27 }= 5 + 104

a_{27 } = 109

Hence 27^{th} term of the sequence is 109.

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