## HOW TO FIND THE SPECIFIED TERM OF AN ARITHMETIC SEQUENCE

How to find the specified term of an arithmetic sequence ?

The formula to find nth term is

an = a + (n - 1)d

Question 1 :

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

125, 120, 115, 110, ……….….

Solution :

First term (a) = 125

Common difference (d) = a2 – a1

d  =  120 – 125

d  =  -25

General term of an A.P

an  =  a + (n - 1) d

an  =  125 + (15 - 1) (-25)

an  =  125 + 14 (-25)

an  =  125 – 350

a15  =  -225

Therefore 15th 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)  =  a2 – a1

d  =  23 ¼ – 24

d  =  (93/4) – 24

d  =  -3/4

an =  a + (n - 1) d

Let us consider 3 as nth term

an  =  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 29th term of A.P.

Question 3 :

Find the 12th 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

an =  a + (n - 1) d

a12 =  √2 + (12 - 1) (2√2)

=  √2 + 11 (2√2)

=  √2 + 22 √2

=  23 √2

Hence 12th of A.P is 23 √2.

Question 4 :

Find the 17th 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

an =  a + (n - 1) d

a17 =  4 + (17 - 1) (5)

a17  =  4 + 16 (5)

a17  =  84

Hence 17th of A.P is 84

Question 5 :

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

an =  a + (n - 1) d

here n = 27

a27  =  5 + (27-1) 4

a27  =  5 + 26 (4)

a27  =  5 + 104

a27  =  109

Hence 27th term of the sequence is 109. Apart from the stuff, if you need any other stuff in math, please use our google custom search here.

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