ARITHMETIC SEQUENCE WORKSHEET SOLUTION1

Arithmetic sequence worksheet solution1 :

Here we are going to see solution of each questions from the arithmetic sequence worksheet.

(1)  The first term of an A.P is 6 and the common difference is 5. Find the A.P and its general term

Solution :

First term = 6

Common difference = 5

 a  =  6

 d  =  5

General form of A.P is a , a + d , a + 2 d , …………….

  6 , (6 + 5) , (6 + 2(5)) , …………..

  6 , 11 , (6 + 10) ,……………….       

Hence the required arithmetic progression is  6, 11, 16 , …………..

(2)  Find the common difference and 15 th term of an A.P 125 , 120 ,115 , 110 , ……….…. 

Solution :

First term = 125

  a = 125

Common difference = t2 – t1

  =  120 – 125

  =  -5

General term of an A.P

(tn) =  a + (n - 1) d

15th term of the A.P  =  125 + (15 - 1) (-5)

=  125 + 14 (-5)

=  125 – 70

t₁₅   =  55

Hence, 15th term of A.P is 55


(3)  Which term of the arithmetic sequence is 24, 23 ¼ ,22 ½, 21 ¾, ………. Is 3?

Solution :

First term = 24

 a = 24

Common difference = t2 – t1

  =  23 ¼ – 24

  =  (93/4) – 24

  =  (93-96)/4

d  =  -3/4

 tn =  a + (n - 1) d

Let us consider 3 as nth term

 tn  =  3

3  =  24 + (n-1) (-3/4)

3 – 24  =  (n-1)  (-3/4)

 (-21 x 4)/(-3)  =  n -1

 84/3  =  n -1

 28  =  n – 1

 28 + 1  =  n

   n  =  29

Hence, 29th term of and A.P is 3.  


(4)  Find the 12th term of the A.P √2 , 3 √2 , 5 √2 , …………

Solution :

First term (a)  =  √2

Common difference (d)  =  3 √2 - √2  =  2 √2

n = 12

General term of an A.P

tn =  a + (n - 1) d

t =  √2 + (12 - 1) (2√2)

 =  √2 + 11 (2√2)

=  √2 + 22 √2

=  23 √2

Hence, 12th of A.P is 23 √2

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